   Chapter 4, Problem 11RE

Chapter
Section
Textbook Problem

Finding a Particular Solution In Exercises 9-12, find the particular solution that satisfies the differential equation and the initial condition. f " ( x ) = 24 x ,     f ' ( − 1 ) = 7 ,   f ( 1 ) = − 4

To determine

To calculate: The solution that fulfills the differential equation f(x)=24x.

Explanation

Given:

The differential equation is, f(x)=24x and initial conditions are, f(1)=7,f(1)=4

Formula used:

The integral property is:xnx=xn+1n+1+c

Calculation:

The given function is solved as,

d2f(x)dx2=24xd(df(x)dx)=24dxdf(x)dx=24xdxdf(x)dx=24x22+c1

It is solved further as,

df(x)=(12x2+c1)dxf(x)=(12x2+c1)d

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