Explanation Given: The differential equation, d y d t = y t 3 − 3 + t Concept Used: To solve a nonhomogeneous linear differential equation of the form, d y d t + g ( t ) y = b ( t ) , first multiply both sides by the integrating factor, μ ( t ) = e ∫ g ( t ) d t , and then integrate both sides to find the general solution. Calculation: Consider the differential equation, d y d t = y t 3 − 3 + t Rewrite the differential equation in nonhomogeneous form to get d y d t − y t 3 − 3 = t Now to solve this nonhomogeneous linear equation, first we compute the integrating factor as shown below: μ ( t ) = e ∫ − 1 t 3 − 3 d t So, on multiplying both sides by the integrating factor, the given differential equation becomes ( e ∫ − 1 t 3 − 3 d t ) d y d t − ( e ∫ − 1 t 3 − 3 d t ) y t 3 − 3 = ( e ∫ − 1 t 3 − 3 d t ) t Here observe that the left side is the derivative of the product of ( e ∫ − 1 t 3 − 3 d t ) and y

Differential Equations (with DE Tools Printed Access Card)

4th Edition

ISBN: 9781133109037

Author: Paul Blanchard

Publisher: Cengage Learning

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Chapter 1.9, Problem 18E

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To find:The general solution of the equation, dydt=yt3−3+t and express it with a few integrals as possible.

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Chapter 1.9, Problem 17E

Chapter 1.9, Problem 19E

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Differential Equations (with DE Tools Printed Access Card)

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The general solution of the equation, d y d t = y t 3 − 3 + t and express it with a few integrals as possible.

Solution Summary: The author explains how to solve a nonhomogeneous linear differential equation by multiplying both sides by the integrating factor.

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To find:The general solution of the equation, dydt=yt3−3+t and express it with a few integrals as possible.

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