   Chapter 5.1, Problem 44E ### 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 ) = 9 x 2 ;   f ( 0 ) = − 1

To determine

To calculate: The particular solution of differential equation f'(x)=9x2 with initial condition f(0)=1.

Explanation

Given Information:

The differential equation is f'(x)=9x2 and the initial condition is f(0)=1.

Formula used:

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

Calculation:

Consider the differential equation, f'(x)=9x2.

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

f'(x)dx=9x2dxf(x)=9(x2+12+1)+C=9(x33)+C=3x3+C

The provided initial condition is f(0)=1

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