What is the solution for (D^3-D^2+D-1)y=4sin(x) ?

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

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(D^3-D^2+D-1)y=4sin(x)

(D^{3} - D^{2} + D - 1) y = 4 sin (x)

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

Solution steps

(D^{3} - D^{2} + D - 1) y = 4 sin (x)

Solve linear ODE:

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

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

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