What is the solution for y^{''}+3y^'+2y=6e^t,y(0)=1,y^'(0)=2 ?

The solution for y^{''}+3y^'+2y=6e^t,y(0)=1,y^'(0)=2 is y=e^{-t}-e^{-2t}+e^t

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y^{''}+3y^'+2y=6e^t,y(0)=1,y^'(0)=2

y^{^{''}} + 3 y^{^{'}} + 2 y = 6 e^{t}, y (0) = 1, y^{^{'}} (0) = 2

y = e^{- t} - e^{- 2 t} + e^{t}

Solution steps

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

Solve linear ODE:

y = e^{- t} - e^{- 2 t} + e^{t}

y = e^{- t} - e^{- 2 t} + e^{t}

What is the solution for y^{''}+3y^'+2y=6e^t,y(0)=1,y^'(0)=2 ?
The solution for y^{''}+3y^'+2y=6e^t,y(0)=1,y^'(0)=2 is y=e^{-t}-e^{-2t}+e^t