What is the solution for y^{''}+y=6xsin(x) ?

The solution for y^{''}+y=6xsin(x) is y=c_{1}cos(x)+c_{2}sin(x)-(3x^2cos(x))/2+(3xsin(x))/2

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y^{''}+y=6xsin(x)

y^{^{''}} + y = 6 x sin (x)

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

Solution steps

y^{''} (x) + y = 6 x sin (x)

Solve linear ODE:

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

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

y^{^{''}} + 6 y^{^{'}} + 13 y = 4 x^{2} - 5 x + 2 + 3 e^{x}

y^{^{''}} - 2 y^{^{'}} - 35 y = 13 sin (x) - e^{3 x} + 1

y^{^{''}} + 4 y = cos (x), y (0) = 6, y^{^{'}} (0) = - 6

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{x}}{2 x}

y^{^{''}} - 2 y^{^{'}} - 3 y = 2 e^{x} - 10 sin (x)

What is the solution for y^{''}+y=6xsin(x) ?
The solution for y^{''}+y=6xsin(x) is y=c_{1}cos(x)+c_{2}sin(x)-(3x^2cos(x))/2+(3xsin(x))/2