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I have trouble solving the following differential equation.

I am trying to learn how to solve that form of DEs.

The DE is:

x^{2}*dy/dx = y^{2}

There are no initial-value problem, but the solution should be given such that y is defined for all x.

The most important for me is to learn how to solve this type of DE.

I tried solving it using the separable equation way.

x^{2}*dy/dx = y^{2}--> dy/y^{2}= dx/x^{2}and then integrate both sides to get -1/y = -1/x + C --> -y = -x + 1/C --> y = x - 1/C but apparently this doesn't solve the equation...

Hope you guys can help me.

Thanks in advance.

Sincerely,

Mr. Fest

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# Differential equation x^2*y'=y^2

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