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

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

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D(D^2+1)y=sin(x)

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} - 2 y^{^{''}} - 5 y^{^{'}} + 6 y = 2 e^{x} (1 - 6 x)

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

x^{^{''}} + 3 x^{^{'}} + 33 x = 11 cos (5 t)

y^{^{''}} + 10 y^{^{'}} + 16 y = 12 cos (2 x) + 4 sin (2 x)

y^{^{'''}} - y^{^{''}} - 12 y^{^{'}} = x - 2 x e^{- 3 x}

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