   Chapter 5, Problem 18RE ### 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 15–18, find the particular solution that satisfies the differential equation and the initial condition. f ' ( x ) = x 3 − 7 x 2 ;   f ( 2 ) = 7

To determine

To calculate: The particular solution that satisfied the differential equation and initial condition f(x)=x37x2 and  f(2)=7.

Explanation

Given Information:

The provided differential equation f(x)=x37x2.

The initial condition f(2)=7

Formula used:

The power rule of integrals:

undu=un+1n+1+C (for n1)

Here, u is function of x.

The property of Intro-differential:

df(x)dxdx=f(x)

Calculation:

Consider the derivative equation:

f(x)=x37x2

Rewrite the integrand as:

df(x)dx=x3x27x2=x7x2

Apply, integration on both sides:

df(x)dxdx=(x7x2)dx+C=(x)dx(7

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