Question

In this probelm y = 1 / (x^2 + c) is a one-parameter family of solutions of the first-order DE y' + 2xy^2 = 0.

1. Find a solution of the first-order IVP consisting of this differential equation and the given initial condition. y(3) = 1/8

Answer 1

`y=(1)/(x^2-1)`

Explanation:

We are given that a family of solutions of the first order DE

`y=(1)/(x^2+c)`

DE

`y'+2xy^2=0`

`y(3)=(1)/(8)`

Substitute x=3

`(1)/(8)=(1)/(3^2+c)`

`3^2+c=8`

`9+c=8`

`c=8-9=-1`

Substitute the value of c

`y=(1)/(x^2-1)`

This is the solution of given IVP.