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)

(d^{2} - 2 d - 3) y = 5

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

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

y^{^{'''}} - 3 y^{^{''}} + 4 y^{^{'}} - 2 y = e^{x}

y^{^{''}} - 6 y^{^{'}} + 9 y = 2, y^{^{'}} (0) = 17

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)