Hello, it's actually my first time posting a thread on this site so I hope you'll forgive me if I do not post as I should. Here is the problem I've got :

Solve the differential equation y''=(y'^2-1)/y with y(1) = 1 and y(2) = 7. I tried different methods but none seemed to be a help in the case. I hope you'll help me solve it. I thank you in advance for your answers.