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} )}

\frac{d V}{d t} = 20 - \frac{5}{100} V, V (0) = 0

y^{^{'}} = x \cdot y - x - 2 \cdot y + 2

(1 + x^{4}) d y + x (1 + 4 y^{2}) d x = 0, y (1) = 1

\frac{d x}{d t} = 12 \cdot x \cdot t

\frac{d y}{d x} = 12 y x^{2}

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))}