What is the solution for (d^2y)/(dx^2)+9y=3sin(x) ?

The solution for (d^2y)/(dx^2)+9y=3sin(x) is y=c_{1}cos(3x)+c_{2}sin(3x)+3/8 sin(x)

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(d^2y)/(dx^2)+9y=3sin(x)

\frac{d ^{2} y}{d x ^{2}} + 9 y = 3 sin (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{3}{8} sin (x)

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 9 y = 3 sin (x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{3}{8} sin (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{3}{8} sin (x)

y^{^{''}} - 7 y^{^{'}} + 12 y = sin (x) - cos (x)

y^{^{''}} + 6 y^{^{'}} + 5 y = 10 cos (x)

(D^{3} - 2 D + 4) y = e^{x} cos (x)

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

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

What is the solution for (d^2y)/(dx^2)+9y=3sin(x) ?
The solution for (d^2y)/(dx^2)+9y=3sin(x) is y=c_{1}cos(3x)+c_{2}sin(3x)+3/8 sin(x)