Chapter 6.1, Problem 6E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Verifying a Solution In Exercises 5–10, verify that the function is a solution of the differential equation.Function Differential Equation y = e − 2 x                 3 y ' + 5 y = − e − 2 x

To determine
Whether the function y=e2x is a solution for the differential equation 3y'+5y=e2x.

Explanation

Given:

i) The function: y=e2x

ii) The differential equation: 3y'+5y=e2x

Explanation:

A function y=e2x has been provided.

The rules of differentiation to be used on the function are as follows:

a) ddx(emx)=memx,m being a constant.

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

y'=dydx=dd</

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