   Chapter 5.3, Problem 10QY ### 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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# In Exercises 10 and 11, find the particular solution that satisfies the differential equation and the initial condition. f ' ( x ) = 16 x ;   f ( 0 ) = 1

To determine

To calculate: The particular solution that satisfied the differential equation and initial condition f(x)=16x and f(0)=1.

Explanation

Given Information:

The provided first derivative f(x)=16x.

The boundary condition f(0)=1

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:

f(x)=16x

Rewrite the integrand as:

df(x)dx=16x

Apply, integration on both sides:

df(

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