What is the solution for yy^'=xy^2-x-y^2+1 ?

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

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yy^'=xy^2-x-y^2+1

y y^{^{'}} = x y^{2} - x - y^{2} + 1

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

Solution steps

y y^{'} (x) = x y^{2} - x - y^{2} + 1

Solve separable ODE:

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

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

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