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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + y = sin (8 x)

y^{^{''}} - 6 y^{^{'}} + 5 y = t e^{2 t}, y (0) = 2, y^{^{'}} (0) = 3

y^{^{'''}} + 12 y^{^{''}} - 13 y = x e^{x} + 5 x

y^{^{''}} + y = 2, y (0) = 0

y^{^{''}} + 5 y^{^{'}} - 24 y = - 92 t + 48 t^{2}

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