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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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 ( 2 + e x )

To determine
Whether the function y=x2(2+ex) is a solution for the differential equation xy'2y=x3ex;x>0

Explanation

Given:

i) The function: y=x2(2+ex).

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

Explanation:

The function y=x2(2+ex) 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 emy/em with respect to x, the following is derived:

y'=dydx=ddx[x2(2+ex)]=ddx(2x2+x2ex)

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