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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{1}{6} y^{^{''}} + 6 y = tan (6 t) - \frac{1}{2} e^{2 t}

9 y^{^{''}} - y = x e^{\frac{x}{3}}, y (0) = 1, y (0) = 0

(D^{2} + 1) y = - t

4 y^{^{''}} + 36 y = csc^{3} (x)

(d^{2} - 4 d + 5) y = (x + 1)^{3}

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