What is the solution for y^{''}+3^2y=6*sin(3x) ?

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

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y^{''}+3^2y=6*sin(3x)

y^{^{''}} + 3^{2} y = 6 \cdot sin (3 x)

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

Solution steps

y^{''} (x) + 3^{2} y = 6 \cdot sin (3 x)

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = x e^{2 x}

y^{^{''}} - 2 y^{^{'}} + y = x^{3} + 3 x

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

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

y^{^{''}} - 4 y = \frac{x + 5 e ^{2 x}}{e ^{2 x}}

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