A First Course in Differential Equations with Modeling Applications (11th Edition)

Chapter 1

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Write the differential equation in the form of a ... more

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On matching the differential equation with the ... more

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Write the differential equation in the form of ... more

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On matching the differential equation with the ... more

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Write the differential equation in the form of ... more

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In the differential equation , the highest order ... more

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Write the differential equation in the form of th... more

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Write the differential equation in the form of the... more

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Non linear in and linear in . ; Rearrange the ... more

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Non linear in and linear in . ; Rearrange the ... more

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Determine the derivative of with respect to the ... more

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Determine the derivative of with respect to .... more

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Determine the derivative of the equation with ... more

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Determine the derivative of the equation with ... more

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The function will be defined only when . The ... more

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The function can be written as .The domain of the... more

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The function can be defined only when .The domain... more

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The function can be defined only when .The domain... more

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The function can be written as . Differentiate ... more

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Differentiate the function with respect to .The ... more

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Differentiate the equation with respect to to ... more

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Differentiate the equation with respect to to ... more

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Differentiate the equation with respect to to ... more

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Differentiate the equation with respect to to ... more

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Differentiate the equation with respect to to ... more

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Differentiate the equation with respect to to ... more

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Differentiate the equation with respect to to ... more

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Differentiate the equation with respect to to ... more

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Substitute 0 for in the equation to determine ... more

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The piecewise-defined function provides different ... more

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; Differentiate the equation with respect to to... more

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; Differentiate the equation with respect to to... more

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; Differentiate the equation with respect to to... more

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; Differentiate the equation with respect to to... more

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; Differentiate the equation with respect to to... more

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; Differentiate the equation with respect to to... more

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; Substitute for and 0 for in the differential... more

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; Substitute for and 0 for in the differential... more

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No constant solution. ; Substitute for and 0 for... more

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; Substitute for , 0 for and 0 for in the ... more

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The left hand side and right hand side of the ... more

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The differential equation that does not have any ... more

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The differential equation that does not have any ... more

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The exponential function has the first derivative ... more

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The exponential function has the second derivative... more

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. ; Substitute for in to simplify the equation ... more

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Since the right hand side of the differential ... more

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; The above graph is divided into two parts by ... more

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; The above graph is divided into four parts. The... more

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Differentiate with respect to , to find the .The ... more

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The differential equation becomes undefined when ... more

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Since and are not differentiable at and , ... more

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Yes, is the solution curve that passes through ... more

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The differential equation can be solved by ... more

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Yes, the equation can be converted into the simple... more

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The differential equation is not equivalent to ... more

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; The two-parameter family of solution of the ... more

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y=x∗e5xcos(2x)From calculator:y′=e5x(5xcos(2x)−... more

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is the particular solution of . ; The given ... more

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; Substitute 0 for and for in . ; Substitute -... more

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; Substitute -1 for and 2 for in to determine ... more

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The largest interval over which the solution is ... more

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The largest interval over which the solution is ... more

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The largest interval over which the solution is ... more

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The largest interval over which the solution is ... more

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; The equations and mean that at , the values ... more

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; The equations  and mean that at the values ... more

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; The equations  and mean that at , the values... more

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; The equations and means at the values and .... more

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; The equation and means at the values and .... more

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; The equation and means at the values and .... more

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; The equation  and means at the values and .... more

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; The equation and means at the values and .... more

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, . ; The first-order differential equation can ... more

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, . ; The first-order differential equation can ... more

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Half-plane is defined by either or . ; The ... more

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, or , . ; The differential equation can be ... more

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Half-plane defined by either or . ; The ... more

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On the entire -plane. ; The differential equation... more

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The region defined by , or  .  ; Substitute for... more

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or . ; Substitute for in the equation to obtain... more

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Any region on -plane does not contain the point... more

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Region with or . ; Substitute for in to obtain... more

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Yes. ; The differential equation can be written ... more

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No. ; The differential equation can be written as... more

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The theorem does not guarantee the presence of an ... more

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The theorem does not guarantee the presence of an ... more

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From the plot, it can be inferred that , and . ... more

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; Substitute 0 for and 0 for in the equation , ... more

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; Substitute 0 for and 0 for in the equation , ... more

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; Differentiate the equation with respect to , ... more

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; Differentiate the equation with respect to , ... more

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No solution. ; Differentiate the equation with ... more

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; The slope of the curve is expressed by the ... more

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The pink color curve represents a plausible ... more

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Differentiate the equation , with respect to .... more

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; As the graph of the solution is tangent to ... more

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It is because the solution of the differential ... more

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The rate at Which the population that of a country... more

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; Consider that represents the date of birth and... more

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; Consider represents the rate of birth and ... more

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; Consider represents the rate of birth of fish ... more

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   ; From the graph, it can be observed that the ... more

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; The general equation for the cosine curve is . ... more

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; The total number of students in an isolated ... more

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; Let the number of people who have not adopted ... more

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; is the amount of salt in the container at time... more

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; is the amount of salt in the container at time... more

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; is the amount of salt in the container at time... more

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; Substitute for concentration of salt inflow, ... more

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; 1 foot consists of .Evaluate the radius of hole... more

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; 1 foot consists of .Evaluate the radius of hole... more

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; The rate of change of current is given by the ... more

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; The current flowing in the circuit due to ... more

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; The gravitational force acting on the sky ... more

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; Substitute for , and for height or ... more

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; The force acting on the spring is , where is ... more

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; The restoring force acting on the spring is ... more

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; The thrust force acts in the upward direction... more

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; Substitute for , and for earth in the ... more

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; Mass of the earth in terms of radius and ... more

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  ; The rate at which a subject is memorized is ... more

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; The amount of study material forgotten is ... more

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  ; Let the rate of drug increase in the ... more

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; Let be the distance of the motorboat from the ... more

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; in terms of is .The rate of change of is ... more

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. ; The differential equation is . Simplify and ... more

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should be less than zero as the temperature ... more

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; The differential equation is or .The rate of ... more

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.The solution is periodic in nature. ; The ... more

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; The rate of change of height is constant . So... more

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dA/dt= -0.0004332A(t)A(t) = (dA/dt)/0.0004332Given... more

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Step 1. Question is not defined. Step 2. Hence no ... more

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; Let .Differentiate the equation with respect ... more

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; Let .Differentiate the equation with respect ... more

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and . ; Let .Differentiate with respect to to ... more

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and . ; Let .Differentiate with respect to , to ... more

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, , and . ; Differentiate with respect to to ... more

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, , and . ; Differentiate with respect to to ... more

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Differentiate the functions , , , and with ... more

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and , here, and are constants. ; The ... more

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and . ; The differential equation holds true if... more

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; The slope of the tangent line is the first ... more

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; The slope of the tangent line is the first ... more

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For , the interval is .For , the interval is . ; ... more

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Substitute 1 for and -1 for in to evaluate the ... more

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7 ; Substitute -1 for and 4 for in the ... more

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Differentiate the equation with respect to .... more

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Differentiate the equation with respect to .... more

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Differentiate the equation with respect to .... more

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Differentiate the equation with respect to .... more

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Multiply both sides of the equation by .... more

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Multiply both sides of the equation by .... more

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Divide both sides of the equation by .... more

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Differentiate the equation by differentiating the... more

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Differentiate the equation with respect to both ... more

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Differentiate the equation with respect to both ... more

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Differentiate the equation with respect to .... more

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Take logarithm on both sides of the equation .... more

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; Determine the first derivative of the equation... more

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; Determine the first derivative of the equation... more

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; Determine the first derivative of the equation... more

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; Determine the first derivative of the equation... more

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and . ; The peak of the graph is at the point . ... more

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; The formula to calculate the volume of water in... more

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