What is the solution for (dy)/(dt)=2y-3e^{-t} ?

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

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(dy)/(dt)=2y-3e^{-t}

\frac{d y}{d t} = 2 y - 3 e^{- t}

y = \frac{1}{e ^{t}} + c_{1} e^{2 t}

Solution steps

\frac{d y}{d t} = 2 y - 3 e^{- t}

Solve linear ODE:

y = \frac{1}{e ^{t}} + c_{1} e^{2 t}

y = \frac{1}{e ^{t}} + c_{1} e^{2 t}

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