Question

In problems 13 to 15, find a solution(or solutions) of the differential equation not obtainable by specializing the constant in your solution of the original problem. Hint: See Example 3.

14. Problem 8.

Short answer

Answer

The solution is $y=0$.

Step-by-step solution

Given information

The given differential equation is $y\text{'}+2x{y}^2=0$

Definition of differential equation

A differential equation is an equation that contains at least onederivative of an unknown function, either an ordinary derivative or a partial derivative.

Solve the differential equation

Separate the variables in problem 8 to get

$\frac{dy}{y^2}=-2xdx$.

The general solution of this differential equation is

$y=\frac{1}{\left(x^2+C\right)}$.

Now, $\frac{dy}{y^2}$is not valid for $y=0$.

$y=0$is a solution of this differential equation that cannot be obtained by any choice of

C.

Therefore, the solution is $y=0$.