What is the solution for (dy)/(dx)(xy)y=1,x=0 ?

The solution for (dy)/(dx)(xy)y=1,x=0 is y=\sqrt[3]{3ln(x)+c_{1}}

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(dy)/(dx)(xy)y=1,x=0

\frac{d y}{d x} (x y) y = 1, x = 0

y = 3 3 ln (x) + c_{1}

Solution steps

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

Solve separable ODE:

y = 3 3 ln (x) + c_{1}

y = 3 3 ln (x) + c_{1}

2 t (d y) + y^{2} (d t) = 0

\frac{d x}{d t} = - \frac{x}{924}

\frac{d y}{d x} = \frac{10 + 19 x}{x y ^{2}}

\frac{d y}{d x} = \frac{( 2 x + 3 )}{( 2 y - 2 )}

\frac{d y}{d x} = \frac{( x x ^{2} + 1 )}{y e ^{y}}

What is the solution for (dy)/(dx)(xy)y=1,x=0 ?
The solution for (dy)/(dx)(xy)y=1,x=0 is y=\sqrt[3]{3ln(x)+c_{1}}