Obtaining General Solution of ODE

[Munir M]

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?

 

[rock.freak667]

I believe you can however, just make sure that you re-write it as dy/dx = +/- y/xAlso 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]

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.

 

[Munir M]

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

Thanks guys!