   Chapter 12.5, Problem 1CP ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Given f ' ( x ) = 2 x − [ 1 / ( x + 1 ) ] , f ( 0 ) = 4 ,(a) find the general solution to the differential equation.(b) find the particular solution that satisfies f ( 0 )   =   4 .

(a)

To determine

To calculate: The general solution of differential equation f(x)=2x[1(x+1)] if f(0)=4.

Explanation

Given Information:

The provided function of is f(x)=2x[1(x+1)] and the function satisfy f(0)=4.

Formula used:

The power rule of integration:

xndx=xn+1n+1+C

The integration of logarithmic:

dxx=ln|x|+C

Calculation:

Consider the provided function

f(x)=2x[1(x+1)]

Integrate the provided function as:

f(x)=

(b)

To determine

To calculate: The particular solution of differential equation f(x)=2x[1(x+1)] if f(0)=4.

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