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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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