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**Home Assignment 2 / Re: problem4 (20)**

« **on:**January 19, 2019, 07:24:22 PM »

We can make the substitution $y = 3x - C$ because we are restricting $u(x, y)$ to the characteristic curves, so I believe we can treat $y$ as equal to $3x - C$ when finding the general solution. We do this because we need the $xydx$ totally in terms of $x$ or we will not be able to integrate both sides. After integrating, we have to get rid of $C$ by replacing it with $3x-y$ again because we want our final solution $u$ to be a function of $x$ and $y$, not of $C$. $C$ is just a constant but it is still in terms of $x, y$ by the characteristic curves.

$C$ is a constant only along integral curves. V.I.

$C$ is a constant only along integral curves. V.I.