Homework Answers
Given differential equation is
ux+uy+uz=0.
We can write above equation as
By variable separation PDE's for above equation are
x'+ax=0 ,y'+by=0 and z'+cz=0.
And solution for each one will be in the form c1e-kt.
Here,we have three variables in the form x,y and z in place of t.
Finally,General solution become
u(x,y,z)=(c1e-ax)(c2e-by)(c3e-cz).
Given new variables are
x=£,y=¥+£ and z=¢+£.
Now,substitute above given relations in the general solution
Finally,General solution become
u(£,¥,¢)=(c1e-a£)(c2e-b(¥+£))(c3e-c(¢+£)).
Let us assume coefficient values as 1
u(£,¥,¢)=e-3£.e-¥.e-¢.
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