What is the solution for x^{''}+81x=sin(7t) ?

The solution for x^{''}+81x=sin(7t) is x=c_{1}cos(9t)+c_{2}sin(9t)+1/32 sin(7t)

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x^{''}+81x=sin(7t)

x^{^{''}} + 81 x = sin (7 t)

x = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{32} sin (7 t)

Solution steps

x^{''} (t) + 81 x = sin (7 t)

Solve linear ODE:

x = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{32} sin (7 t)

x = c_{1} cos (9 t) + c_{2} sin (9 t) + \frac{1}{32} sin (7 t)

y^{^{''}} + 2 y^{^{'}} = t e^{- t}

y^{^{''}} + 4 y^{^{'}} + 5 y = 2 cos (x) - 2 sin (x)

y^{^{''}} - y^{^{'}} - 2 y = 2 x^{2} + 5

(D + 3) y = x + 1

y^{^{''}} - y = \frac{( 4 e ^{- x} )}{( 1 - e ^{- 2 x} )}

What is the solution for x^{''}+81x=sin(7t) ?
The solution for x^{''}+81x=sin(7t) is x=c_{1}cos(9t)+c_{2}sin(9t)+1/32 sin(7t)