What is the solution for y^{''}+3y^'+2y=10u,y(0)=0,y^'(0)=0 ?

The solution for y^{''}+3y^'+2y=10u,y(0)=0,y^'(0)=0 is y=-10ue^{-t}+5ue^{-2t}+5u

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y^{''}+3y^'+2y=10u,y(0)=0,y^'(0)=0

y^{^{''}} + 3 y^{^{'}} + 2 y = 10 u, y (0) = 0, y^{^{'}} (0) = 0

y = - 10 u e^{- t} + 5 u e^{- 2 t} + 5 u

Solution steps

y^{''} (t) + 3 y^{'} (t) + 2 y = 10 u

Solve linear ODE:

y = - 10 u e^{- t} + 5 u e^{- 2 t} + 5 u

y = - 10 u e^{- t} + 5 u e^{- 2 t} + 5 u

What is the solution for y^{''}+3y^'+2y=10u,y(0)=0,y^'(0)=0 ?
The solution for y^{''}+3y^'+2y=10u,y(0)=0,y^'(0)=0 is y=-10ue^{-t}+5ue^{-2t}+5u