Question

The general solution to the PDE
x
@u
@x
°
y
@u
@y
+
u
=
x
is
u
(
x;y
) =
x
2
+
1
x
d
(
xy
), for a general function
d
. Find the solution of this PDE
that satisØes
u
(
x;x
) = 3
x
3
+
x
2
for all
x
. (Once you have the solution, you should
check that it actually satisØes the condition.)