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

The solution for (dy)/(dt)+3y=t+e^{-2t} is y=(3t-1)/9+1/(e^{2t)}+(c_{1})/(e^{3t)}

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

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

y = \frac{3 t - 1}{9} + \frac{1}{e ^{2 t}} + \frac{c _{1}}{e ^{3 t}}

Solution steps

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

Solve linear ODE:

y = \frac{3 t - 1}{9} + \frac{1}{e ^{2 t}} + \frac{c _{1}}{e ^{3 t}}

y = \frac{3 t - 1}{9} + \frac{1}{e ^{2 t}} + \frac{c _{1}}{e ^{3 t}}

What is the solution for (dy)/(dt)+3y=t+e^{-2t} ?
The solution for (dy)/(dt)+3y=t+e^{-2t} is y=(3t-1)/9+1/(e^{2t)}+(c_{1})/(e^{3t)}