I stumbled upon this differential equation while thinking of a physics problem.
I found two solutions using wolframalpha.
And when I plot it, the result is magically accurate (according to my intuition). So, I know it's right.
My question is, how can I learn to solve this particular differential equation? Is there a procedural approach to arrive at this solution or does solving it mean plugging in the guess and fiddling with the free parameters to arrive at one particular solution?