   Chapter 5.1, Problem 46E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding a Particular Solution In Exercises 43–50, find the particular solution that satisfies the differential equation and the initial condition. See Example 6. f ' ( x ) = 1 5 x − 2 ;   f ( 10 ) = − 10

To determine

To calculate: The particular solution of differential equation f'(x)=15x2 with initial condition f(10)=10.

Explanation

Given Information:

The differential equation is f'(x)=15x2 and the initial condition is f(10)=10.

Formula used:

The simple power rule of integration xndx=xn+1n+1+C.

Calculation:

Consider the differential equation, f'(x)=15x2.

Integrate the provided differential equation, use the simple power rule of integration xndx=xn+1n+1+C.

f'(x)dx=(15x2)dxf(x)=15xdx+(2)dx=15(x1+11+1)2x+C=110x22x+C

The provided initial condition is f(10)=10

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