What is the general solution of df/(dx dy) = x * df/dx + (B+1) * f + C?

Question

Where B,C are constants?

I meant d^2 f / (dx dy)

B & C are constants

Answer 1

I don't think this problem is properly posed. The term df/(dx dy) does not make sense. Do you mean d^2f/(dx dy) ? If so the solution is
f = A(y^B)exp(xy) + D/x^(B+1) - C/(B+1)
where A and D are constants. I finally got the first term using the Laplace transform on y. Let me know if you want all the details.

This is a difficult problem. I hope it's for an advanced course!