   Chapter 12.5, Problem 12E ### 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 2 x + 1         y ( 0 ) = e

To determine

To calculate: The particular solution to the differential equation y=e2x+1 if y(0)=e.

Explanation

Given Information:

The provided differential equation is y=e2x+1 and the value is y(0)=e.

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=e2x+1

Rewrite the differential equation as,

dydx=e2x+1dy=e2x+1dx

Integrate both sides of the equation,

dy=e2x+1dxy=e2x+1dx

If 2x+1=t then,

2dx=dtdx=12dt,

Substitute 2x+1=t and dx=12dt in the equation y=e2x+1dx

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