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

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

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y^{''}+y=xsin(x)

y^{^{''}} + 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

y^{''} (x) + 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}

y^{^{'''}} + y^{^{''}} + 4 y^{^{'}} + 4 y = 100 x sin (3 x)

y^{^{''}} + 4 y = sin (2 t) + t cos (t)

y^{^{''}} + 4 y^{^{'}} + 3 y = 5 e^{2 x}

y^{^{''}} - 12 y^{^{'}} + 35 y = - 40 e^{- 3 t}

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 x} ln (1 + x^{2})

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