What is the solution for (d^3+d)*y=cos(x) ?

The solution for (d^3+d)*y=cos(x) is y=c_{1}+c_{2}cos(x)+c_{3}sin(x)-(xcos(x))/2

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(d^3+d)*y=cos(x)

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

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) - \frac{x cos ( x )}{2}

Solution steps

(d^{3} + d) y = cos (x)

Solve linear ODE:

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) - \frac{x cos ( x )}{2}

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) - \frac{x cos ( x )}{2}

(d^{3} + 3 d^{2} - 4) y = sinh^{2} (x) + 7

y^{^{''}} + 4 y^{^{'}} = 12 x^{2} - 10 x - 16

(d^{2} + 6 d + 9) y = 5 e^{3} x

(d^{3} - 2 d^{2} - 3 d + 10) y = 40 cos (x)

y^{^{''}} + 3 y^{^{'}} + 2.25 y = 8 t^{3} + 64

What is the solution for (d^3+d)*y=cos(x) ?
The solution for (d^3+d)*y=cos(x) is y=c_{1}+c_{2}cos(x)+c_{3}sin(x)-(xcos(x))/2