MHB Verify a function is a solution.

[ISITIEIW]

Verify that x^2 + y^2 = cy is a solution of dy/dx = (2xy)/(x^2-y^2) where c is a constant.

I don't know how i should start this problem. I've done a couple DE questions but nothing like this.. Thanks

 

[Ackbach]

One trick I learned (from Jester) when doing these problems is to eliminate the constant $c$, whenever possible, for first-order. To do that, simply solve for the constant and then take the necessary derivative. Your goal here is to plug the function and its derivative into the DE and show that you get equality.

 

[lfdahl]

View attachment 1897

and

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the last identity inserted in the DE:

View attachment 1898

which is in agreement with the first equation.There might be a much better way to show that y fulfills the DE.