Show the relation is an implicit solution of the DiffEQ

[_N3WTON_]

Homework Statement

Differential equation: 2xyy' = x^2 + y^2
Relation: y^2 = x^2 - cx

Homework Equations

The Attempt at a Solution

Hello, I can normally solve this problems with ease; however, I am having trouble with this particular problem. I have performed the implicit differentiation to get: (2yy' = 2x - c). However, I can't seem to figure out where to go from here. I am thinking that perhaps there is some obvious simplification that I am missing. If somebody can point me in the right direction I'd greatly appreciate it. Thanks.

 

[vela]

Multiply 2yy' = 2x-c by x so that the lefthand sides look the same and use 2x^2 = x^2+x^2.

 

[_N3WTON_]

thank you very much, I figured I was missing something somewhat obvious