What is the solution for (dy)/(dx)=4y^3 ?

The solution for (dy)/(dx)=4y^3 is y=sqrt(-1/(2(4x+c_{1)))},y=-sqrt(-1/(2(4x+c_{1)))}

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(dy)/(dx)=4y^3

\frac{d y}{d x} = 4 y^{3}

y = - \frac{1}{2 ( 4 x + c _{1} )}, y = - - \frac{1}{2 ( 4 x + c _{1} )}

Solution steps

\frac{d y}{d x} = 4 y^{3}

Solve separable ODE:

y = - \frac{1}{2 ( 4 x + c _{1} )}, y = - - \frac{1}{2 ( 4 x + c _{1} )}

y = - \frac{1}{2 ( 4 x + c _{1} )}, y = - - \frac{1}{2 ( 4 x + c _{1} )}

(2 x y + y) d x + (x^{2} - x) d y = 0

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

x \to 0 + lim (12 cos (12 x))

x y^{^{'}} + 2 y = sin (x), y (π) = \frac{1}{π}

\int \frac{1}{r ^{2} - x ^{2}} d x

What is the solution for (dy)/(dx)=4y^3 ?
The solution for (dy)/(dx)=4y^3 is y=sqrt(-1/(2(4x+c_{1)))},y=-sqrt(-1/(2(4x+c_{1)))}