What is the solution for y^{''}+9y=6cos(3x)+9sin(3x) ?

The solution for y^{''}+9y=6cos(3x)+9sin(3x) is y=c_{1}cos(3x)+c_{2}sin(3x)+xsin(3x)-(3xcos(3x))/2

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y^{''}+9y=6cos(3x)+9sin(3x)

y^{^{''}} + 9 y = 6 cos (3 x) + 9 sin (3 x)

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

Solution steps

y^{''} (x) + 9 y = 6 cos (3 x) + 9 sin (3 x)

Solve linear ODE:

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

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

y^{^{''}} - 4 y = 6 e^{(- t)}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{'''}} + 7 y^{^{''}} + 8 y^{^{'}} - 16 y = - 2 e^{x} - 2

y^{^{''}} + 3 y^{^{'}} + 2 y = 42 \cdot e^{5} x

x^{^{'''}} + 3 x^{^{''}} + x^{^{'}} + 3 x = t^{2}

y^{^{''}} + 3 y^{^{'}} + 15.25 y = e^{t}

What is the solution for y^{''}+9y=6cos(3x)+9sin(3x) ?
The solution for y^{''}+9y=6cos(3x)+9sin(3x) is y=c_{1}cos(3x)+c_{2}sin(3x)+xsin(3x)-(3xcos(3x))/2