What is the solution for (dy)/(dx)=e^xy^3 ?

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

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(dy)/(dx)=e^xy^3

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = (5 x + 1) (y + 11), y (0) = 0

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

e^{2 x} (2 cos (y) d x - sin (y) d y) = 0, y (0) = 0

sinh (x) d x + y^{- 1} cosh (x) d y = 0

\frac{d y}{d x} = \frac{2 cos ( 2 x )}{3 + 2 y}

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