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

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

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

\frac{d y}{d x} = 2 \cdot (x^{2}) \cdot (y^{2})

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

Solution steps

\frac{d y}{d x} = 2 \cdot (x^{2}) \cdot (y^{2})

Solve separable ODE:

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

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

d x - \frac{d y}{1 + y ^{2}} = 0

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

x d x - y d y = x y (x d y - y d x)

\frac{d y}{d x} = \frac{sin ( x )}{sec ^{2} ( y )}

y^{^{'}} = \frac{y ^{4}}{x ^{6}}

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