What is the solution for e^{kt}((dy)/(dt)+ky)=0 ?

The solution for e^{kt}((dy)/(dt)+ky)=0 is y=e^{-kt+c_{1}}

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e^{kt}((dy)/(dt)+ky)=0

e^{k t} (\frac{d y}{d t} + k y) = 0

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

Solution steps

e^{k t} (\frac{d y}{d t} + k y (t)) = 0

Solve separable ODE:

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

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

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What is the solution for e^{kt}((dy)/(dt)+ky)=0 ?
The solution for e^{kt}((dy)/(dt)+ky)=0 is y=e^{-kt+c_{1}}