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

The solution for y^2y^'=xln(x^2) is y=\sqrt[3]{(6x^2ln(x)-3x^2+c_{1})/2}

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y^2y^'=xln(x^2)

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

y = 3 \frac{6 x ^{2} ln ( x ) - 3 x ^{2} + c _{1}}{2}

Solution steps

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

Solve separable ODE:

y = 3 \frac{6 x ^{2} ln ( x ) - 3 x ^{2} + c _{1}}{2}

y = 3 \frac{6 x ^{2} ln ( x ) - 3 x ^{2} + c _{1}}{2}

x^{2} y^{^{'}} - y - y^{2} = 0

\frac{d y}{d x} y = x e^{- 6 x} + 6 e^{- x} + x^{7}

\frac{d}{d x} (x^{2} + y^{2}) = \frac{d}{d x} (9)

\frac{d y}{d x} = y, y (1) = 1

y = e^{\frac{3}{2 x}} \frac{d y}{d x}

What is the solution for y^2y^'=xln(x^2) ?
The solution for y^2y^'=xln(x^2) is y=\sqrt[3]{(6x^2ln(x)-3x^2+c_{1})/2}