   Chapter 6.1, Problem 28E

Chapter
Section
Textbook Problem

Determining a Solution: In Exercises 23-30, determine whether the function is a solution of the differential equation x y ' - 2 y = x 3 e x ; x > 0 . y = x 2 e x + sin   x + cos   x

To determine
Whether the function y=x2ex+sinx+cosx is a solution of the differential equation xy'2y=x3ex;x>0

Explanation

Given:

i) The function is y=x2ex+sinx+cosx.

ii) The differential equation is xy'2y=x3ex;x>0

Explanation:

The function y=x2ex+sinx+cosx has been provided.

The product rule of differentiation has to be used:

ddx(f.g)=f.dgdx+g.dfdx;f and g being functions of x.

On differentiating both sides of y with respect to x, the following is derived:

y'=dydx=ddx(x2ex+sinx+cosx)=ddx(x2ex)+ddx(sinx)

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