2nd order homogeneous ODE

Hello again :)

This time I have a question concerning the 2nd order homogeneous ODE and it's general solutions :)

in the following thread:
Homogeneous Linear Equations

they speak about it as having the general form:

y''[x] +p[x]*y'[x]+q[x]*y''[x] = 0

in the case where p[x] and q[x] are constant, one can easily obtain the general solution using the characteristic polynomial :)

my question: What do we do in all the other cases, when p[x] and q[x] are any other functions of x? (unfortunately they do not give a general solution to it in the thread)

with best regards, Marine

maybe try reading this..
Second-Order Ordinary Differential Equation -- from Wolfram MathWorld

it's a sort of complicated with all those substitutions but I think I got it :)

Thanks a lot


Btw, does anyone know if such ODEs are ever to be found in nature?