What is the solution for y^{''}+81y=2sin(x) ?

The solution for y^{''}+81y=2sin(x) is y=c_{1}cos(9x)+c_{2}sin(9x)+1/40 sin(x)

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y^{''}+81y=2sin(x)

y^{^{''}} + 81 y = 2 sin (x)

y = c_{1} cos (9 x) + c_{2} sin (9 x) + \frac{1}{40} sin (x)

Solution steps

y^{''} (x) + 81 y = 2 sin (x)

Solve linear ODE:

y = c_{1} cos (9 x) + c_{2} sin (9 x) + \frac{1}{40} sin (x)

y = c_{1} cos (9 x) + c_{2} sin (9 x) + \frac{1}{40} sin (x)

y^{^{''}} + 8 y^{^{'}} + \frac{1}{2} y = 10 sin (4 x)

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = 6 \cdot e^{x} + 10 cos (x)

y^{^{''}} + 3 y^{^{'}} + 2 y = H (2)

y^{^{''}} + n^{2} y = \frac{2}{n ^{2} π} ((- 1)^{n} - 1) cos (t)

y^{^{''}} - 10 y^{^{'}} + 25 y = 75 t + 295

What is the solution for y^{''}+81y=2sin(x) ?
The solution for y^{''}+81y=2sin(x) is y=c_{1}cos(9x)+c_{2}sin(9x)+1/40 sin(x)