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}

y^{^{''}} + 500 y^{^{'}} + 20000 y = 1100

y^{^{''}} + 2 y^{^{'}} - 8 y = x + 1

y^{^{''}} - y^{^{'}} - 6 y = 15 sin (3 x)

y^{^{''}} - 4 y^{^{'}} + 3 y = 10 e^{3 x}

y^{^{''}} - y^{^{'}} = 1 + 2 x + e^{x} + sin (x) + cos (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