   Chapter 12.5, Problem 29E ### 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 29-36, find the particular solution to each differential equation. 29. d y d x = x 2 y 3 when x = 1 ,   y = 1

To determine

To calculate: The particular solution to the differential equation dydx=x2y3 when x=1, y=1.

Explanation

Given Information:

The provided differential equation is dydx=x2y3 and the values are x=1, y=1.

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,

dydx=x2y3

Rearrange the equation as,

y3dy=x2dx

Integrate both sides of the equation,

y3dy=x2dxy3+13+1=x2+12+1+Cy44=x33+C

The provided values are x=1, y=1

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