What is the solution for y^'=((y^2))/(x^3) ?

The solution for y^'=((y^2))/(x^3) is y=-(2x^2)/(-1+2c_{1)x^2}

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y^'=((y^2))/(x^3)

y^{^{'}} = \frac{( y ^{2} )}{x ^{3}}

y = - \frac{2 x ^{2}}{- 1 + 2 c _{1} x ^{2}}

Solution steps

y^{'} (x) = \frac{( y ^{2} )}{x ^{3}}

Solve separable ODE:

y = - \frac{2 x ^{2}}{- 1 + 2 c _{1} x ^{2}}

y = - \frac{2 x ^{2}}{- 1 + 2 c _{1} x ^{2}}

\frac{\partial}{\partial x} (3 x^{2} y^{2} + 1)

\int \frac{1}{10 x - 3} d x

y = (3 x - 1) (- 3 x^{2} - 4)^{- 3}

\int sec^{2} (x) sec (x) d x

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

What is the solution for y^'=((y^2))/(x^3) ?
The solution for y^'=((y^2))/(x^3) is y=-(2x^2)/(-1+2c_{1)x^2}