Can anyone show me how to make this:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]xy=c\left( y+\sqrt{y^2-x^2}\right)[/tex]

Look like this:

[tex]y^2-cx=y\sqrt{ y^2-x^2}[/tex]

These were given as the answers to an ODE problem.

I'm assuming that they are equivalent because they are presented in the answer as:

[itex]y^2-cx=y\sqrt{ y^2-x^2}[/itex], or equivalently [itex]xy=c\left( y+\sqrt{y^2-x^2}\right) [/itex]

I got the second answer but I can't figure out how to algebraically manipulated it to make look like the first.

Any takers?

P.S. I'm not certain if it can even be done algebraically. It might have something to do with the methods that were used to solve the ODE. But if they are equivalent answers it should be possible to obtain one from the other using just algebra shouldn't it?

My algebra skills suck! :yuck:

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# Methods that were used to solve the ODE

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