trouble with finding the explicit equation of the particular solution

Hi qguys, I need help with some math problems (I am studying for an exam..) can anyone please help me with these???

If you could explain how to do these step by step, rather than just give me the answer, I would really appreciate it.
Attachment 23979

and 2nd problem:

Attachment 23980

Are you sure there's not a typo in the first one? You have two equations there, not one...

i didnt make an error.. there are 2 equations,thats why i am confused and dont know how to get started... its example of exam from last year given by our teacher, unfortunately he doesnt want to give answers :(