What is the solution for y^{'''}+y^{''}+y^'+y=x^2+2x-2 ?

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

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y^{'''}+y^{''}+y^'+y=x^2+2x-2

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = x^{2} + 2 x - 2

y = c_{1} e^{- x} + c_{2} cos (x) + c_{3} sin (x) + x^{2} - 4

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} cos (x) + c_{3} sin (x) + x^{2} - 4

y = c_{1} e^{- x} + c_{2} cos (x) + c_{3} sin (x) + x^{2} - 4

y^{^{''}} - y^{^{'}} = e^{2 x}, y (0) = 0, y (1) = 0

x^{^{''}} + 4 x = cos (2 t)

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

y^{^{''}} + 4 y = - 5, y (\frac{π}{8}) = - \frac{1}{4}, y^{^{'}} (\frac{π}{8}) = 2

y^{^{''}} + 7 y^{^{'}} + 6 y = 3 sin (2 t)

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