solution to non-homogenenous PDE using method of characteristics?

Dear all,

I am very new to this forum after a friend recommended it. I am preparing for my final graduation exam there is one question I can not solve (Sweating)

I was hoping perhaps someone could help me

a= a(x,y)

a*axy = ax*ay = xy (so a differentiated w.r.t. x and y)

a(x,0) = x

I need to find the solution of a using the method of characteristics. I only knew how to solve it using direct integration but this was not allowed (Crying)

Thanks in advance

Greetings from Barcelona