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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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 ) = 20 x 3 4 x ; f ( 1 ) = 3

To determine

To calculate: The particular solution of differential equation f'(x)=20x34x with initial condition f(1)=3.

Explanation

Given Information:

The differential equation is f'(x)=20x34x and the initial condition is f(1)=3.

Formula used:

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

The sum rule of the integration [f(x)+g(x)]dx=f(x)dx+g(x)dx.

Calculation:

Consider the differential equation, f'(x)=20x34x.

Integrate the provided differential equation, use the sum rule of the integration [f(x)+g(x)]dx=f(x)dx+g(x)dx.

f'(x)dx=(20x34x)dxf(x)=20x3dx+(4x)dx=20x3dx4xdx

Integrate the further, use the simple power rule of integration xndx=xn+1n+1+C

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