   Chapter 12.5, Problem 20E ### 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 15-28, find the general solution to the given differential equation. 20.   d y = ( x 2 y 3 + x y 3 ) d x

To determine

To calculate: The general solution to the differential equation dy=(x2y3+xy3)dx.

Explanation

Given Information:

The provided differential equation is dy=(x2y3+xy3)dx.

Formula used:

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

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

Calculation:

Consider the differential equation, dy=(x2y3+xy3)dx

Rearrange the equation as,

dy=y3(x2+x)dxdyy3=(x2+x)dxy3dy=(x2+x)dx

Integrate both sides of the equation,

y3dy=(x2+x)dx

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