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

The solution for y^{''}+y=3xsin(x) is y=c_{1}cos(x)+c_{2}sin(x)-(3x^2cos(x))/4+(3xsin(x))/4

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y^{''}+y=3xsin(x)

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

y = c_{1} cos (x) + c_{2} sin (x) - \frac{3 x ^{2} cos ( x )}{4} + \frac{3 x sin ( x )}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - \frac{3 x ^{2} cos ( x )}{4} + \frac{3 x sin ( x )}{4}

y = c_{1} cos (x) + c_{2} sin (x) - \frac{3 x ^{2} cos ( x )}{4} + \frac{3 x sin ( x )}{4}

x^{^{''}} + 6 x^{^{'}} + 25 x = t e^{- t}

y^{^{''}} + 9 y = 2 sec (3 x)

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- x} - sin (2 x)

y^{^{''}} - 2 y^{^{'}} + y = t^{2} - 1

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

What is the solution for y^{''}+y=3xsin(x) ?
The solution for y^{''}+y=3xsin(x) is y=c_{1}cos(x)+c_{2}sin(x)-(3x^2cos(x))/4+(3xsin(x))/4