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Method of characteristics

  • #1

Homework Statement



solve using method of characteristics
[tex]

y \frac{ \partial u}{ \partial x} - x \frac{ \partial u}{ \partial y}= 1

[/tex] where u(x,0) = 0 for 0<x<infinity


The Attempt at a Solution



[tex]

\frac{ \partial y}{ \partial x} = \frac{x}{y}

[/tex] which gives [tex]y^2+x^2= k [/tex] the projected characteristic. but its the second part that is giving me trouble when i go to find [tex]

\frac{ \partial u}{ \partial x} = \frac{1}{y}

[/tex] which doesnt work out right...any suggestion anyone?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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hi gtfitzpatrick! :smile:

(have a curly d: ∂ :wink:)

∂y/∂x = x/y gives y2 minus x2 = k :wink:
 
  • #3
hi gtfitzpatrick! :smile:

(have a curly d: ∂ :wink:)

∂y/∂x = x/y gives y2 minus x2 = k :wink:
my mistake it should have read [/SIZE]

∂y/∂x = -x/y gives y2 + x2 = k

but dont know how to work the second part?
 
  • #4
oh and hi back :smile:
 

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