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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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