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

The solution for y^{''}+81y=2sin(at) is y=c_{1}cos(9t)+c_{2}sin(9t)+(2sin(at))/(-a^2+81)

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

y^{^{''}} + 81 y = 2 sin (a t)

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{2 sin ( a t )}{- a ^{2} + 81}

Solution steps

y^{''} (t) + 81 y = 2 sin (a t)

Solve linear ODE:

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{2 sin ( a t )}{- a ^{2} + 81}

y = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{2 sin ( a t )}{- a ^{2} + 81}

y^{^{''}} + 19 y = 4 e^{x}

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

y^{^{''}} - y^{^{'}} = 8 e^{x}

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 16 e^{7} t, y (0) = 7, y^{^{'}} (0) = 4

What is the solution for y^{''}+81y=2sin(at) ?
The solution for y^{''}+81y=2sin(at) is y=c_{1}cos(9t)+c_{2}sin(9t)+(2sin(at))/(-a^2+81)