What is the solution for ((df)/(dy))f(y)=e^{-y} ?

The solution for ((df)/(dy))f(y)=e^{-y} is f(y)=sqrt(-2e^{-y)+c_{1}},f(y)=-sqrt(-2e^{-y)+c_{1}}

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((df)/(dy))f(y)=e^{-y}

(\frac{df}{d y}) f (y) = e^{- y}

f (y) = - 2 e^{- y} + c_{1}, f (y) = - - 2 e^{- y} + c_{1}

Solution steps

(\frac{df}{d y}) f = e^{- y}

Solve separable ODE:

f (y) = - 2 e^{- y} + c_{1}, f (y) = - - 2 e^{- y} + c_{1}

f (y) = - 2 e^{- y} + c_{1}, f (y) = - - 2 e^{- y} + c_{1}

4 y^{3} \frac{d y}{d x} - 5 x^{2} + 3 x = 0

y ln (x) \frac{d x}{d y} = (\frac{y + 1}{x})

y \cdot \frac{d y}{d x} = 5 x (y^{2} + 2)^{4}

t^{^{'}} + t = 0

3 y^{2} \frac{d y}{d x} = 5 x

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