What is the solution for y^{''}-36y=24sin(6t) ?

The solution for y^{''}-36y=24sin(6t) is y=c_{1}e^{6t}+c_{2}e^{-6t}-1/3 sin(6t)

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y^{''}-36y=24sin(6t)

y^{^{''}} - 36 y = 24 sin (6 t)

y = c_{1} e^{6 t} + c_{2} e^{- 6 t} - \frac{1}{3} sin (6 t)

Solution steps

y^{''} (t) - 36 y = 24 sin (6 t)

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{- 6 t} - \frac{1}{3} sin (6 t)

y = c_{1} e^{6 t} + c_{2} e^{- 6 t} - \frac{1}{3} sin (6 t)

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

y^{^{''}} + 7 y^{^{'}} + 11 y = 11 x^{3} + 10 x^{2} - 8 x + 9

y^{^{''}} - 10 y^{^{'}} + 25 y = t^{- 9} e^{5 t}

x^{^{''}} + x = 2 cos (t)

y^{^{'''}} - y^{^{''}} = 3 e^{x} + sin (x)

What is the solution for y^{''}-36y=24sin(6t) ?
The solution for y^{''}-36y=24sin(6t) is y=c_{1}e^{6t}+c_{2}e^{-6t}-1/3 sin(6t)