What is the solution for y^{''}-y=9.5cos(t) ?

The solution for y^{''}-y=9.5cos(t) is y=c_{1}e^t+c_{2}e^{-t}-4.75cos(t)

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y^{''}-y=9.5cos(t)

y^{^{''}} - y = 9.5 cos (t)

y = c_{1} e^{t} + c_{2} e^{- t} - 4.75 cos (t)

Solution steps

y^{''} (t) - y = 9.5 cos (t)

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- t} - 4.75 cos (t)

y = c_{1} e^{t} + c_{2} e^{- t} - 4.75 cos (t)

y^{^{''}} + 2 y^{^{'}} + y = e^{t} ln (t)

y^{^{''}} + 9 y^{^{'}} = 5 t

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- t}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 9 y = - 12 sec (3 t)

y^{^{''}} + 4 y = g (t), y (0) = 5, y^{^{'}} (0) = 16

What is the solution for y^{''}-y=9.5cos(t) ?
The solution for y^{''}-y=9.5cos(t) is y=c_{1}e^t+c_{2}e^{-t}-4.75cos(t)