What is the solution for y^{''}+y=cos(x)+3sin(2x) ?

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

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y^{''}+y=cos(x)+3sin(2x)

y^{^{''}} + y = cos (x) + 3 sin (2 x)

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

Solution steps

y^{''} (x) + y = cos (x) + 3 sin (2 x)

Solve linear ODE:

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

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

y^{^{''}} + 49 y = x^{2} cos (7 x) + x e^{- 7 x}

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

y^{^{''}} + 7 y^{^{'}} + 10 y = - 10 + e^{4 t}

y^{^{''}} - y = cos (2 x)

y^{^{''}} + 2 y^{^{'}} + 2 y = (e^{(- x)}) \cdot cos (x)

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