What is the solution for (dy)/(dt)=-4y+3e^{-t} ?

The solution for (dy)/(dt)=-4y+3e^{-t} is y= 1/(e^t)+(c_{1})/(e^{4t)}

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(dy)/(dt)=-4y+3e^{-t}

\frac{d y}{d t} = - 4 y + 3 e^{- t}

y = \frac{1}{e ^{t}} + \frac{c _{1}}{e ^{4 t}}

Solution steps

\frac{d y}{d t} = - 4 y + 3 e^{- t}

Solve linear ODE:

y = \frac{1}{e ^{t}} + \frac{c _{1}}{e ^{4 t}}

y = \frac{1}{e ^{t}} + \frac{c _{1}}{e ^{4 t}}

What is the solution for (dy)/(dt)=-4y+3e^{-t} ?
The solution for (dy)/(dt)=-4y+3e^{-t} is y= 1/(e^t)+(c_{1})/(e^{4t)}