What is the solution for y^'=-x/y+((x^2+y^2))/y ?

The solution for y^'=-x/y+((x^2+y^2))/y is y=sqrt(-x^2+c_{1)e^{2x}},y=-sqrt(-x^2+c_{1)e^{2x}}

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y^'=-x/y+((x^2+y^2))/y

y^{^{'}} = - \frac{x}{y} + \frac{( x ^{2} + y ^{2} )}{y}

y = - x^{2} + c_{1} e^{2 x}, y = - - x^{2} + c_{1} e^{2 x}

Solution steps

y^{'} (x) = - \frac{x}{y} + \frac{( x ^{2} + y ^{2} )}{y}

Solve Bernoulli ODE:

y = - x^{2} + c_{1} e^{2 x}, y = - - x^{2} + c_{1} e^{2 x}

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What is the solution for y^'=-x/y+((x^2+y^2))/y ?
The solution for y^'=-x/y+((x^2+y^2))/y is y=sqrt(-x^2+c_{1)e^{2x}},y=-sqrt(-x^2+c_{1)e^{2x}}