Chapter 6.1, Problem 24E

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361

Chapter
Section

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361
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 3 − e − x

To determine

Whether the function y=x3ex is a solution for the differential equation xy'2y=x3ex;x>0

Explanation

Given:

i) The function y=x3ex

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

The function y=x3ex has been provided.

Following rules of differentiation need to be used:

(i) ddx(emx)=memx;m being a constant.

(ii) d/dx(xn)=nx(n1)

(iii) ddx(fg)=dfdxdgdx;f and g being functions of x

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