how can i solve coupled differential of equation with rkf or another method

maple.mw

A1 , A2, A3 ??

i want to dsolve frome this equation . but i cant

1.mw

hello. i want to write this function with  "for"loop. but i don't know
1.mw

hello. i want to write this functionT with  "for"loop. but i don't know
 

e.mw

hello. how can i solve this integral. thank you