What is the solution for y^'=y^3e^{-x} ?

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

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y^'=y^3e^{-x}

y^{^{'}} = y^{3} e^{- x}

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

Solution steps

y^{'} (x) = y^{3} e^{- x}

Solve separable ODE:

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

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

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