   Chapter 12.5, Problem 11E ### 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

# In Problems 11-14, find the particular solution. 12.   y ' = e x − 3         y ( 0 ) = 2

To determine

To calculate: The particular solution to the differential equation y=ex3 if y(0)=2.

Explanation

Given Information:

The provided differential equation is y=ex3 and the value is y(0)=2.

Formula used:

Solution of the differential equation dy=f(x)dx is y=f(x)dx.

The integration formula of exponential function is exdx=ex+C.

Calculation:

Consider the differential equation, y=ex3

Rewrite the differential equation as,

dydx=ex3dy=ex3dx

Integrate both sides of the equation,

dy=ex3dxy=ex3dx

If x3=t then dx=dt,

Substitute x3=t and dx=dt in the equation y=ex3dx

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