   Chapter 5.1, Problem 48E ### 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 ) = x + 2 x ;     f ( 4 ) = 25

To determine

To calculate: The particular solution of differential equation f'(x)=x+2x with initial condition f(4)=25.

Explanation

Given Information:

The differential equation is f'(x)=x+2x and the initial condition is f(4)=25.

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)=x+2x.

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=(x+2x)dxf(x)=xdx+2xdx=x12dx+2xdx

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

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