   Chapter 12.5, Problem 14E ### 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. 14.   d y = ( x 2 − 1 x + 1 ) d x         y ( 0 ) = 1 3

To determine

To calculate: The particular solution to the differential equation dy=(x21x+1)dx if y(0)=13.

Explanation

Given Information:

The provided differential equation is dy=(x21x+1)dx and the value is y(0)=13.

Formula used:

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

The logarithmic formula of integration is 1x+adx=ln|x+a|+C, where a is any real number.

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

Calculation:

Consider the differential equation, dy=(x21x+1)dx

Integrate both sides of the equation,

dy=(x21x+1)dxy=x2+12+1ln|x+1|

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