   Chapter 5.1, Problem 51E ### 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 51–54, find a function f that satisfies the differential equation and the initial conditions. f " ( x ) = 2 ,   f ' ( 2 ) = 5 ,   f ( 2 ) = 10

To determine

To calculate: The particular solution of differential equation f''(x)=2 with initial condition f'(2)=5 and f(2)=10.

Explanation

Given Information:

The differential equation is f''(x)=2, and the initial condition are f'(2)=5 and f(2)=10.

Formula used:

The constant rule of integration kdx=kx+C.

The simple power rule of integration xndx=xn+1n+1+C.

Calculation:

Consider the differential equation, f''(x)=2.

Integrate the provided differential equation, use the constant rule of integration kdx=kx+C.

f''(x)dx=2dxf'(x)=2x+C1

Substitute 2 for x in differential equation f'(x)=2x+C1.

f'(2)=2(2)+C1=4+C1

Substitute 5 for f'(2) in above differential equation to get the value of constant C1.

5=4+C1C1=54=1

Substitute 1 for C1 in the function f'(x)=2x+C1.

f'(x)=2x+1

Integrate the above differential equation f'(x)=2x+1, use the simple power rule of integration xndx=xn+1n+1+C

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