What is the solution for θ^{''}(t)-θ(t)=t ?

The solution for θ^{''}(t)-θ(t)=t is θ(t)=c_{1}e^t+c_{2}e^{-t}-t

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θ^{''}(t)-θ(t)=t

θ^{^{''}} (t) - θ (t) = t

θ (t) = c_{1} e^{t} + c_{2} e^{- t} - t

Solution steps

θ^{''} (t) - θ (t) = t

Solve linear ODE:

θ (t) = c_{1} e^{t} + c_{2} e^{- t} - t

θ (t) = c_{1} e^{t} + c_{2} e^{- t} - t

y^{^{'''}} + y^{^{'}} = sec (x)

y^{^{''}} + 7 y^{^{'}} - 8 y = 13 e^{2 x}, y (0) = 1, y^{^{'}} (0) = 1

y^{^{'''}} - 11 y^{^{''}} + 35 y^{^{'}} - 25 = 0

\frac{d ^{2} y}{d t ^{2}} + 2 y = cos (7 t)

y^{^{''}} + 3 y = 2

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