What is the solution for y^{''}+3y^'+2y=6e^{2t} ?

The solution for y^{''}+3y^'+2y=6e^{2t} is y=c_{1}e^{-t}+c_{2}e^{-2t}+1/2 e^{2t}

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y^{''}+3y^'+2y=6e^{2t}

y^{^{''}} + 3 y^{^{'}} + 2 y = 6 e^{2 t}

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

Solution steps

y^{''} (t) + 3 y^{'} (t) + 2 y = 6 e^{2 t}

Solve linear ODE:

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

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

y^{^{'''}} + 2 y^{^{''}} - 11 y^{^{'}} - 12 y = 4

y^{^{''}} + y^{^{'}} - 42 y = - 130 t + 84 t^{2}

\frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 32 y = 32 H (t)

d, d (t) = - t^{2} + 5 t

y^{^{''}} + 2 y^{^{'}} + 2 y = 2 (x + 1)^{2}

What is the solution for y^{''}+3y^'+2y=6e^{2t} ?
The solution for y^{''}+3y^'+2y=6e^{2t} is y=c_{1}e^{-t}+c_{2}e^{-2t}+1/2 e^{2t}