What is the solution for y^{''}+3y^'+2y=1,2e^ty(0)=2,y^'(0)=3 ?

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

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y^{''}+3y^'+2y=1,2e^ty(0)=2,y^'(0)=3

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

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

Solution steps

y^{''} (t) + 3 y^{'} (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}

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