What is the solution for (dy)/(dt)+e^ty=12e^t ?

The solution for (dy)/(dt)+e^ty=12e^t is y=-e^{-e^t-c_{1}}+12

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(dy)/(dt)+e^ty=12e^t

\frac{d y}{d t} + e^{t} y = 12 e^{t}

y = - e^{- e^{t} - c_{1}} + 12

Solution steps

\frac{d y}{d t} + e^{t} y = 12 e^{t}

Solve separable ODE:

y = - e^{- e^{t} - c_{1}} + 12

y = - e^{- e^{t} - c_{1}} + 12

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What is the solution for (dy)/(dt)+e^ty=12e^t ?
The solution for (dy)/(dt)+e^ty=12e^t is y=-e^{-e^t-c_{1}}+12