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

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

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(dy)/(dx)=3x^2y^3

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

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

Solution steps

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

Solve separable ODE:

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

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

3 y^{4} - 1 + 12 x y^{3} \frac{d y}{d x} = 0

y^{^{'}} - 10 y^{^{'}} + 25 y = 0

\frac{d y}{d x} - 0.075 y = - 9000

y^{^{'}} = e^{y + t}

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

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