What is the solution for (d^2y)/(dt^2)+3((dy)/(dt))+2y=1 ?

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

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(d^2y)/(dt^2)+3((dy)/(dt))+2y=1

\frac{d ^{2} y}{d t ^{2}} + 3 (\frac{d y}{d t}) + 2 y = 1

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

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 3 (\frac{d y}{d t}) + 2 y = 1

Solve linear ODE:

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

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

\int_{1}^{\infty} \frac{x}{6 + x ^{2}} d x

\frac{d}{d x} (0.001 x^{3} - 0.14 x^{2} + 7 x + 160)

[(z - 1)^{3} (z + 1)^{2}] - 1

\int \frac{t ^{2} - 3}{- t ^{3} + 9 t + 1} d t

3 x

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