What is the solution for x^{''}-9x=-13cos(2t) ?

The solution for x^{''}-9x=-13cos(2t) is x=c_{1}e^{3t}+c_{2}e^{-3t}+cos(2t)

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x^{''}-9x=-13cos(2t)

x^{^{''}} - 9 x = - 13 cos (2 t)

x = c_{1} e^{3 t} + c_{2} e^{- 3 t} + cos (2 t)

Solution steps

x^{''} (t) - 9 x = - 13 cos (2 t)

Solve linear ODE:

x = c_{1} e^{3 t} + c_{2} e^{- 3 t} + cos (2 t)

x = c_{1} e^{3 t} + c_{2} e^{- 3 t} + cos (2 t)

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

y^{^{''}} - 4 y = sinh (2 x)

y^{^{''}} + 6 y^{^{'}} + 5 y = 36 e^{x}, y (0) = - 2

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{t}, y (0) = 1, y (0) = - 1

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

What is the solution for x^{''}-9x=-13cos(2t) ?
The solution for x^{''}-9x=-13cos(2t) is x=c_{1}e^{3t}+c_{2}e^{-3t}+cos(2t)