What is the solution for (dy)/(dt)+e^ty=10e^t ?

The solution for (dy)/(dt)+e^ty=10e^t is y=-e^{-e^t-c_{1}}+10

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(dy)/(dt)+e^ty=10e^t

\frac{d y}{d t} + e^{t} y = 10 e^{t}

y = - e^{- e^{t} - c_{1}} + 10

Solution steps

\frac{d y}{d t} + e^{t} y = 10 e^{t}

Solve separable ODE:

y = - e^{- e^{t} - c_{1}} + 10

y = - e^{- e^{t} - c_{1}} + 10

What is the solution for (dy)/(dt)+e^ty=10e^t ?
The solution for (dy)/(dt)+e^ty=10e^t is y=-e^{-e^t-c_{1}}+10