What is the solution for y^{''}=x(y^')^2 ?

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

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

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

y = - \frac{2 arctan ( \frac{1}{c _{1}} x )}{c _{1}} + c_{2}

Solution steps

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

Solve using substitution:

y = - \frac{2 arctan ( \frac{1}{c _{1}} x )}{c _{1}} + c_{2}

y = - \frac{2 arctan ( \frac{1}{c _{1}} x )}{c _{1}} + c_{2}

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