XUx + yUy =0 with u(0, y) = e-y² ,du du a. (x, y) = 0 `dx'dy' XUx + yUy = 0 %3D У yields Uy х you can do some integral calculus to get Ux Uy dy yields У * yields dx dx х dy dx In(y) = In(x) + C eln(y) = eln(x)+c у %3D хес У %3 хс (-) yields x = y

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The question is to 

Solve xUx + yUy = 0 

with u(o,y)=e-y^2

and so far i have set up the following to find the general solution

<du/dx , du/dy> * <x,y> = 0

... i have included the rest in a photo

I have general solution y=xec

y=xc , x=y(1/c) and this is where I get all messed up, not sure how to proceed. 

XUx + yUy =0 with u(0, y) = e-y²
,du du
a. (x, y) = 0
`dx'dy'
XUx + yUy = 0
%3D
У
yields
Uy
х
you can do some integral calculus to get
Ux
Uy
dy
yields
У
* yields
dx
dx
х
dy
dx
In(y) = In(x) + C
eln(y) = eln(x)+c
у %3D хес
У %3 хс
(-)
yields x = y
Transcribed Image Text:XUx + yUy =0 with u(0, y) = e-y² ,du du a. (x, y) = 0 `dx'dy' XUx + yUy = 0 %3D У yields Uy х you can do some integral calculus to get Ux Uy dy yields У * yields dx dx х dy dx In(y) = In(x) + C eln(y) = eln(x)+c у %3D хес У %3 хс (-) yields x = y
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