# Obtaining General Solution of ODE

## Homework Statement

So they want me to obtain the general solution for this ODE.

## Homework Equations

I have managed to turn it into d^2y/dx^2=(y/x)^2.

## The Attempt at a Solution

My question is, can I simply make d^2y/dx^2 into (dy/dx)^2, cancel the power of 2 from both sides of the equation and then integrate it normally?

If not, why?

## Answers and Replies

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rock.freak667
Homework Helper
I believe you can however, just make sure that you re-write it as dy/dx = +/- y/x

Also note the distinction that d^2y/dx^2 = d/dx(dy/dx) i.e. differentiating dy/dx wrt x and (dy/dx)*(dy/dx) = (dy/dx)^2.

Mark44
Mentor
I believe you can however, just make sure that you re-write it as dy/dx = +/- y/x
In other words, solve dy/dx = y/x as well as dy/dx = -y/x.

In other words, solve dy/dx = y/x as well as dy/dx = -y/x.
Thanks guys!