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

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

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y^{''}+y=2xcos(x)

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

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

Solution steps

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

Solve linear ODE:

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

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

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