What is the solution for y^{'''}+y^{''}+4y^'+4y=4x+4 ?

The solution for y^{'''}+y^{''}+4y^'+4y=4x+4 is y=c_{1}e^{-x}+c_{2}cos(2x)+c_{3}sin(2x)+x

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y^{'''}+y^{''}+4y^'+4y=4x+4

y^{^{'''}} + y^{^{''}} + 4 y^{^{'}} + 4 y = 4 x + 4

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

Solution steps

y^{'''} (x) + y^{''} (x) + 4 y^{'} (x) + 4 y = 4 x + 4

Solve linear ODE:

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

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

y^{^{''}} + 8 y^{^{'}} + 16 = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 e^{2 t}, y^{^{'}} (0) = 5, y (0) = - 3

y^{^{''}} - 4 y^{^{'}} + 8 y = 16 x

(d^{2} + 1) y = x^{3}

y^{^{''}} + 4 y = 8 x^{2} + 9 x

What is the solution for y^{'''}+y^{''}+4y^'+4y=4x+4 ?
The solution for y^{'''}+y^{''}+4y^'+4y=4x+4 is y=c_{1}e^{-x}+c_{2}cos(2x)+c_{3}sin(2x)+x