What is the solution for y^{''}+y=cos(x)+4 ?

The solution for y^{''}+y=cos(x)+4 is y=c_{1}cos(x)+c_{2}sin(x)+(xsin(x))/2+4

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y^{''}+y=cos(x)+4

y^{^{''}} + y = cos (x) + 4

y = c_{1} cos (x) + c_{2} sin (x) + \frac{x sin ( x )}{2} + 4

Solution steps

y^{''} (x) + y = cos (x) + 4

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + \frac{x sin ( x )}{2} + 4

y = c_{1} cos (x) + c_{2} sin (x) + \frac{x sin ( x )}{2} + 4

y^{^{''}} - 2 y^{^{'}} + 5 = 0

y^{^{''}} - 8 y^{^{'}} + 20 y = 200 x^{2} - 39

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = e^{4 x}

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

y^{^{''}} + 2 y^{^{'}} - 8 y = 3 e^{- 2 x} - e^{- x}

What is the solution for y^{''}+y=cos(x)+4 ?
The solution for y^{''}+y=cos(x)+4 is y=c_{1}cos(x)+c_{2}sin(x)+(xsin(x))/2+4