Examining Solutions of Non-Linear DEs

[neelakash]

Homework Statement

Given y1=x^2 and y2=1 are two solutions of the DE
y"=(x/y)y'

Are the functions -y1 and y1 and y2 also the solutions of the equation?If not why?

Homework Equations

The Attempt at a Solution

I cannot see how to proceed.However,I can see that it is a non-linear DE of
2nd degree where we cannot simply sum the solutions to have another solution...
That might explain the case that y1+y2 is not a solution...

what about the first case,i.e -y1?

 

[neutrino]

Do you end up with an identity when you substitute -y1, (-y1)' and (-y1)'' the DE?

 

[neelakash]

OK what I am getting is a wrong thing:-2=2!
So,this shows -y1 cannot be a solution.

Perhaps I was thinking in unnecessary complicated manner.

What about the 2nd part? that is y1+y2?
Am I correct there?

 

[neutrino]

Yes you are. You can check by doing what you did for 1.