What is the solution for ((dy)/(dt)-e^{-t}+6)/y =-6,y(0)=-2 ?

The solution for ((dy)/(dt)-e^{-t}+6)/y =-6,y(0)=-2 is y= 1/(5e^t)-1-6/(5e^{6t)}

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((dy)/(dt)-e^{-t}+6)/y =-6,y(0)=-2

\frac{\frac{d y}{d t} - e ^{- t} + 6}{y} = - 6, y (0) = - 2

y = \frac{1}{5 e ^{t}} - 1 - \frac{6}{5 e ^{6 t}}

Solution steps

\frac{\frac{d y}{d t} - e ^{- t} + 6}{y} = - 6

Solve linear ODE:

y = \frac{1}{5 e ^{t}} - 1 - \frac{6}{5 e ^{6 t}}

y = \frac{1}{5 e ^{t}} - 1 - \frac{6}{5 e ^{6 t}}

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What is the solution for ((dy)/(dt)-e^{-t}+6)/y =-6,y(0)=-2 ?
The solution for ((dy)/(dt)-e^{-t}+6)/y =-6,y(0)=-2 is y= 1/(5e^t)-1-6/(5e^{6t)}