What is the solution for (dy)/(dx)=-(5x^2)/(2y^2) ?

The solution for (dy)/(dx)=-(5x^2)/(2y^2) is y=\sqrt[3]{-(5x^3)/2+c_{1}}

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(dy)/(dx)=-(5x^2)/(2y^2)

\frac{d y}{d x} = - \frac{5 x ^{2}}{2 y ^{2}}

y = 3 - \frac{5 x ^{3}}{2} + c_{1}

Solution steps

\frac{d y}{d x} = - \frac{5 x ^{2}}{2 y ^{2}}

Solve separable ODE:

y = 3 - \frac{5 x ^{3}}{2} + c_{1}

y = 3 - \frac{5 x ^{3}}{2} + c_{1}

(x^{2} + 1) y^{^{'}} + y^{2} = 0

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

y^{^{'}} = \frac{( 3 t ^{2} + 4 t + 2 )}{( 2 y - 2 )}

y tan (x) \frac{d y}{d x} = (4 + y^{2}) sec (x^{2})

\frac{d y}{d x} = c \cdot y

What is the solution for (dy)/(dx)=-(5x^2)/(2y^2) ?
The solution for (dy)/(dx)=-(5x^2)/(2y^2) is y=\sqrt[3]{-(5x^3)/2+c_{1}}