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I am dealing with a physics problem and as usual an ODE emerged. Namely,

$$\ddot{x} = (\dot{x})^2*C_1 + \dot{x}*x*C_2 + \dot{x}*g_1(t) + \dot{x}*C_3 +x*C_4 + g_2(t) $$

$x(t)$ is the unknown function and $t$ the independent variable. $C_i$ are known constants and $g_i$ known functions of the form $A*sin(9*π*t/5)+B$

I have tried many approaches to solve it explicitly, such as setting $w=\dot{x}/x$ or trying to find a particular solution by assuming $x = A*sin(w*t)+B*t+C$.

Before I attempt to approximate it using a taylor series, I wanted to ask if there is any obvious way of going about solving this that I missed.

A complete answer or a hint are both very welcome. Thank you in adnvance.

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