What is the solution for (d^2y)/(dx^2)+y=cos(x) ?

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

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(d^2y)/(dx^2)+y=cos(x)

\frac{d ^{2} y}{d x ^{2}} + y = cos (x)

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 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 = 3 + cos (2 t)

y^{^{''}} + 4 y = sin^{3} (x)

y^{^{''}} + 3 y^{^{'}} + 2 y = cos (t) - sin (2 t)

y^{^{''}} + 4 y = 8 sin (t)

y^{^{''}} + 3 y^{^{'}} + 2 y = 30 e^{2 x}

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