What is the solution for y^'sqrt(y-x^2y)=-xy ?

The solution for y^'sqrt(y-x^2y)=-xy is y=-1/4 x^2+1/4+c_{1}sqrt(-x^2+1)+c_{1}^2

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y^'sqrt(y-x^2y)=-xy

y^{^{'}} y - x^{2} y = - x y

y = - \frac{1}{4} x^{2} + \frac{1}{4} + c_{1} - x^{2} + 1 + c_{1}^{2}

Solution steps

y^{'} (x) y - x^{2} y = - x y

Solve Bernoulli ODE:

y = - \frac{1}{4} x^{2} + \frac{1}{4} + c_{1} - x^{2} + 1 + c_{1}^{2}

y = - \frac{1}{4} x^{2} + \frac{1}{4} + c_{1} - x^{2} + 1 + c_{1}^{2}

What is the solution for y^'sqrt(y-x^2y)=-xy ?
The solution for y^'sqrt(y-x^2y)=-xy is y=-1/4 x^2+1/4+c_{1}sqrt(-x^2+1)+c_{1}^2