What is the solution for (dy)/(3x+e^x)=e^{-y}dx ?

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

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(dy)/(3x+e^x)=e^{-y}dx

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

y = ln (\frac{3 x ^{2}}{2} + e^{x} + c_{1})

Solution steps

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

Solve separable ODE:

y = ln (\frac{3 x ^{2}}{2} + e^{x} + c_{1})

y = ln (\frac{3 x ^{2}}{2} + e^{x} + c_{1})

csc (x) (x + cot (x))

x^{7} e^{x}

\frac{d y}{d x} = 2 y + a

\int \frac{1}{z + 1}

\frac{d}{d x} (- (x^{2}))

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