Find the solution of the equation uxy = ux

  • Thread starter kasse
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  • #1
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Homework Statement



Find the solution of the equation

uxy = ux

The Attempt at a Solution



ux = p

py = p

ln p = y + c*

p = ce^y

But them, what is u?
 
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Answers and Replies

  • #2
HallsofIvy
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Well, how would you solve the ORDINARY differential equation. dp/dx= p? That's seems to me very easy. Warning: because this is NOT an ordinary differential equation, the "constant" in the solution may be a function of y. Also remember that the general solution to a partial differential equation involves unknown FUNCTIONS.
 
  • #3
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Just integrate wrt. x so that

u(x,y) = e^y Int[c(x)]dx + g(y) where c(x) and g(y) are arbitrary?
 

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