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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

(d^{2} + 4) \cdot y = 4 tan^{2} (x)

y^{^{''}} - 3 y^{^{'}} = x + 3

x^{^{''}} - x^{^{'}} - 2 = 5 cos (2 t)

(d^{2} - 8 d + 20) \cdot y = 100 x^{2} - 26 x \cdot e^{x}

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