I am wondering if there is a general solution for this ODE

$\ddot X +2\gamma \alpha \dot X + (\alpha+S(t)) X = \beta $

the dot represents time derivative, and $\gamma>1$, so it is in the over dumped regime.

It is a form of parametric oscillator, but I am wondering if there may exist a general solution for any function $S(t)$, as there exist for first order systems.

Thanks in advance.

I am wondering if there is a general solution for this ODE

$\ddot X +2\gamma \alpha \dot X + (\alpha+S(t)) X = \beta $

the dot represents time derivative, and $\gamma>1$, so it is in the over-damped regime.

It is a form of parametric oscillator, but I am wondering if there may exist a general solution for any function $S(t)$, as there exist for first order systems.

Thanks in advance.

I am wondering if there is a general solution for this ODE

$\ddot X +2\gamma \alpha \dot X + (\alpha+S(t)) X = \beta $

the dot represents time derivative, and $\gamma>1$, so it is in the over dumped regime.

It is a form of parametric oscillator, but I am wondering if there may exist a general solution for any function $S(t)$.

Thanks in advance.

I am wondering if there is a general solution for this ODE

$\ddot X +2\gamma \alpha \dot X + (\alpha+S(t)) X = \beta $

the dot represents time derivative, and $\gamma>1$, so it is in the over dumped regime.

It is a form of parametric oscillator, but I am wondering if there may exist a general solution for any function $S(t)$, as there exist for first order systems.

Thanks in advance.