# Non-homogenenous PDE: method of characteristics

I am very new here after a friend recommended this site. I am preparing for my final graduation exam there is one question I can not solve:

I was hoping perhaps someone could help me.

$$a= a(x,y)$$ $$a a_{xy} = a_x a_y = xy$$ $$a(x,0) = x$$ (so $a$ differentiated w.r.t. $x$ and $y$).

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

Thanks in advance

Greetings from Barcelona

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Please use TEX for typing the equation. –  doraemonpaul Jan 18 '13 at 0:58
Welcome to math.SE! Here is a quick TeX tutorial. I can try to format your equation properly, but you should check that I did not change its meaning. –  user53153 Jan 18 '13 at 1:36
Thank you so much for editing 5PM indeed, this is indeed the equation! –  Vasquez Jan 18 '13 at 11:10
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