ODE's without constant coefficients are hard to find general solutions to.

One common method is to attempt to find a power series solution centered around your initial conditions. (The other is numerically)

It usually goes something like this suppose that

Note that I am using the to be the constants in the series expansion

Now we need to do the same thing with this gives

Now comes the bad part we need to product of the series

Using the columns gives the series representation

Now just equate coefficients

This gives

Now you should know all of the and the first two your initial conditions and this will give a recurrence relation for all of the coefficients of the power series.