Problem solving a PDE system

Questions
1

Could anyone give me a hint on how to solve (analytically and/or numerically) a system that looks like

[{C1 F1''[x] + C2 (F2'[x] F10'[x] + F20'[x] F1'[x] + F1[x] F20''[x] + F10[x] F2''[x]) + C0 F1[x] == 0,
 C1 F3''[x] + C2 (F2'[x] F30'[x] + F20'[x] F3'[x] + F3[x] F20''[x] + F30[x] F2''[x]) + C0 F3[x] == 0,
 F2''[X] + C3 (F1[x] + F3[x]) == 0},
 {F1[x], F2[x], F3[x]}, x]

where F1(x), F2(x) and F3(x) are the unknown functions, F10(x), F20(x) and F30(x) are known functions and C0, C1, C2, C3 are constants. Any ideas will be much appreciated.

2

shouldn’t be a problem with NDSolve if you provide the known functions and constants.