It does not appear that you are doing anything particularly wrong.
You might be having some accuracy and precision difficulties, because you have one very large coefficient with lots of digits and other very small coefficients that only have a couple of digits precision. Mathematica (roughly) looks at how many digits you provide for each constant and assumes you only know that value to that number of digits. However, even if I change all your coefficients to exact fractions, DSolve cannot find a solution.
But remember, lots of, perhaps even almost all, differential equations just do not have closed form solutions that college students or even Mathematica can find.
If a numerical approximation of your problem would be acceptable then you might look at NDSolve. That will find an approximate solution almost instantly.