Explanation Given: The differential function and initial value is given as, e x d y d x − e x y = x 2 − 1... ( 1 ) y ( 0 ) = 42. Approach: The particular solution of differential equation obtained with the help of integrations and with the help of general form of linear differential equation. The general form of linear differential equation, d y d x + P y = Q ... ( 2 ) Integrating function ( I . F ) = e ∫ P d x ... ( 3 ) The solution of the equation is given by, y ( I . F ) = ∫ Q ( I . F ) d x + C ... ( 4 ) Calculation: The particular solution is calculated as, Rearranging the equation ( 1 ) . d y d x − y = x 2 − 1 e x ... ( 5 ) The equation ( 5 ) is compared with the equation ( 2 ) , we get P = − 1 , Q = x 2 − 1 e x . The value of P put up in the equation ( 3 ) . ( I . F ) = e ∫ − 1 d x ( I . F ) = e − x ... ( 6 ) I.F. and Q value put up in the equation ( 4 ) . y ( e − x ) = ∫ ( x 2 − 1 e x ) ( e − x ) d x + C y ( e − x ) = ∫ ( x 2 − 1 ) ( e − 2 x ) d x + C y e − x = ∫ ( x 2 e − 2 x − e − 2 x ) d x + C y e − x = ∫ x 2 e − 2 x d x − ∫ e − 2 x d x + C y e − x = x 2 e − 2 x − 2 − ∫ e − 2 x − 2 ( 2 x ) d x − e − 2 x − 2 + C y e − x = x 2 e − 2 x − 2 + ∫ x e − 2 x d x + e − 2 x 2 + C Solving the above equation.

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 11.CR, Problem 43CR

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The particular solution of the differential equation exdydx−exy=x2−1.

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Chapter 11.CR, Problem 42CR

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The particular solution of the differential equation e x d y d x − e x y = x 2 − 1.

Solution Summary: The author explains how the particular solution of the differential equation is obtained by integrations and with the help of general form of linear differential.

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To find:

The particular solution of the differential equation exdydx−exy=x2−1.

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Chapter 11 Solutions

The particular solution of the differential equation e x d y d x − e x y = x 2 − 1.

Solution Summary: The author explains how the particular solution of the differential equation is obtained by integrations and with the help of general form of linear differential.

Concept explainers

Videos

To find: The particular solution of the differential equation exdydx−exy=x2−1.

Want to see the full answer?

Chapter 11 Solutions

To find:

The particular solution of the differential equation exdydx−exy=x2−1.