What is the solution for (dy)/(dx)=-x/(y^2) ?

The solution for (dy)/(dx)=-x/(y^2) is y=\sqrt[3]{-(3x^2)/2+c_{1}}

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(dy)/(dx)=-x/(y^2)

\frac{d y}{d x} = - \frac{x}{y ^{2}}

y = 3 - \frac{3 x ^{2}}{2} + c_{1}

Solution steps

\frac{d y}{d x} = - \frac{x}{y ^{2}}

Solve separable ODE:

y = 3 - \frac{3 x ^{2}}{2} + c_{1}

y = 3 - \frac{3 x ^{2}}{2} + c_{1}

y^{^{'}} 1 - x^{2} + 1 - y^{2} = 0

\frac{1}{1 + y ^{2}} y^{^{'}} = x

y^{^{'}} + 2 y t = 0, y (1) = \frac{( e + 3 )}{2}

\frac{d y}{d x} = 14 e^{5 x - 4 y}

(4 x - 8) d x = (6 y - 10) d y

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