1.(a) Solve the given equation by the method of characteristic curves.
(b) Check your answer by plugging it back into the equation.
x ∂u/∂x + y ∂u/∂y = 0
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You should have the explanation of the method of characteristics in your textbook(s) or lecture notes. However, just in case and for the reference here, you can look at web page http://en.wikipedia.org/wiki/Method_of_characteristics
To start, I recommend a change to convenient variables
q = ln(x) and r = ln(y). (1)
Then the PDE becomes
∂u/∂q + ∂u/∂r = 0. ...
A PDE is solve using characteristic curves. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.