In the PDE:
$ yU_y-xU_x=1$
how did the characteristics become $dx\over -x$=$dy \over y$ =$du \over 1$.Can someone please expalin how these charactristic equations were obtained
2026-03-27 01:13:34.1774574014
characteristic equation in pde
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For each one you consider the respective coefficient.
The coefficient of $U_x$ is $-x$, so we get $\frac{dx}{-x}$
The coefficient of $U_y$ is $y$, so we get $\frac{dy}{y}$
Now for $u$ we consider the coefficient on the right hand side of the equation, which is $1$, so we get $\frac{du}{1}$