What is the solution for x^{''}-6x-16x=sin(2t) ?

The solution for x^{''}-6x-16x=sin(2t) is x=c_{1}e^{sqrt(22)t}+c_{2}e^{-sqrt(22)t}-1/26 sin(2t)

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x^{''}-6x-16x=sin(2t)

x^{^{''}} - 6 x - 16 x = sin (2 t)

x = c_{1} e^{22 t} + c_{2} e^{- 22 t} - \frac{1}{26} sin (2 t)

Solution steps

x^{''} (t) - 6 x - 16 x = sin (2 t)

Solve linear ODE:

x = c_{1} e^{22 t} + c_{2} e^{- 22 t} - \frac{1}{26} sin (2 t)

x = c_{1} e^{22 t} + c_{2} e^{- 22 t} - \frac{1}{26} sin (2 t)

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

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

y^{^{''}} + 6 y^{^{'}} + 3 x = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 5 y = 5 sin (x), y (0) = 1, y^{^{'}} (0) = 2

y^{^{'''}} + y^{^{'}} = sec (t), y^{^{'}} (0) = 3, y^{^{''}} (0) = - 2

What is the solution for x^{''}-6x-16x=sin(2t) ?
The solution for x^{''}-6x-16x=sin(2t) is x=c_{1}e^{sqrt(22)t}+c_{2}e^{-sqrt(22)t}-1/26 sin(2t)