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

The solution for y^{'''}+y^{''}+y^'+y=2e^{-t}+3 is y=c_{1}e^{-t}+c_{2}cos(t)+c_{3}sin(t)+e^{-t}t+3

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

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

y = c_{1} e^{- t} + c_{2} cos (t) + c_{3} sin (t) + e^{- t} t + 3

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} cos (t) + c_{3} sin (t) + e^{- t} t + 3

y = c_{1} e^{- t} + c_{2} cos (t) + c_{3} sin (t) + e^{- t} t + 3

y^{^{''}} - 2 y^{^{'}} + 2 y = cos (x)

y^{^{''}} + 5 y^{^{'}} + 4 y = t e^{- t} H (t)

3 y^{^{''}} - 2 y^{^{'}} = t

(D^{4} - 2 D^{2} + 1) Y = cos (x)

D (D^{2} + 1) y = sin (x)

What is the solution for y^{'''}+y^{''}+y^'+y=2e^{-t}+3 ?
The solution for y^{'''}+y^{''}+y^'+y=2e^{-t}+3 is y=c_{1}e^{-t}+c_{2}cos(t)+c_{3}sin(t)+e^{-t}t+3