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Easiest PDE

  • Thread starter PhDorBust
  • Start date
  • #1
143
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Given [tex]\frac{\partial^2 V}{\partial u \partial v} = 0[/tex], the solution is [tex]V_1(u) + V_2(v)[/tex] for arbitrary [tex]V_1 , V_2[/tex].

I solve to get [tex]\frac{\partial V}{\partial u} = V_3(u)[/tex] and then [tex]V = \int V_3(u) du + C[/tex] Where V_3, C are arbitrary.

How could I transform my latter solution into the first solution? Don't V_1, V_2 have to have some properties such as differentiability? (I found this in a physics textbook)
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
try the same method but integrate over the other variable first then equate the two results
 

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