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

Answer:

$y=\frac{1}{x^2-1}$

Step-by-step explanation:

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

$y=\frac{1}{x^2+c}$

DE

$y'+2xy^2=0$

$y(3)=\frac{1}{8}$

Substitute x=3

$\frac{1}{8}=\frac{1}{3^2+c}$

$3^2+c=8$

$9+c=8$

$c=8-9=-1$

Substitute the value of c

$y=\frac{1}{x^2-1}$

This is the solution of given IVP.