   Chapter 12.5, Problem 13E ### 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. 13.   d y = ( 1 x − x ) d x         y ( 1 ) = 0

To determine

To calculate: The particular solution to the differential equation dy=(1xx)dx if y(1)=0.

Explanation

Given Information:

The provided differential equation is dy=(1xx)dx and the value is y(1)=0.

Formula used:

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

The logarithmic formula of integration is 1xdx=ln|x|+C.

The power of x formula of integration is xndx=xn+1n+1+C, where n1.

Calculation:

Consider the differential equation, dy=(1xx)dx

Integrate both sides of the equation,

dy=(1xx)dxy=ln|x|x22+C

The values of x and y for y(1)=0 are 1 and 0 respectively

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