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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{2 x} (cos (x) - 5 sin (x))

y^{^{''}} + 5 y^{^{'}} + 4 y = e^{- t}

y^{^{''}} + 49 y = 11 sec^{2} (7 t)

y^{^{''}} - 10 y^{^{'}} + 25 y = 3 x + 5

y^{^{''}} + y^{^{'}} = 2 x

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