- #1

manenbu

- 103

- 0

## Homework Statement

Solve:

y'''=(y'')

^{2}

## Homework Equations

## The Attempt at a Solution

Basically easy, use the substitution y'' = p and solve through the equations.

I end up having this:

y=-(x+c

_{1})ln|x+c

_{1}| + c

_{2}x + c

_{3}, which is what I listed in the answers as well.

My question is about p≠0 which I get while solving the first integral.

p=y''=0 is a solution to the equation.

y''=0 means y'=c means y=cx+c

Is this included in the solution? I don't think so, and then it should be listed as a solution as well, but it's not. Am I missing something, or it's already in the first solution?