Toronto Math Forum
APM346--2019 => APM346--Lectures & Home Assignments => Home Assignment 2 => Topic started by: Zhiman Tang on January 18, 2019, 07:26:28 PM
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the integral curve is： dt = dx/x
if I integrate both sides, I get t - lnx = c, so the general solution is u = f(t-lnx)
however, it I move x to the left side: xdt = dx, and integrate both sides, I get xt - x = c. You cannot do this, since in ODE , describing integral curves, $x$ and $t$ are not independent. V.I.
the general solution becomes u = f(xt-x)
I feel the second approach is wrong, but I cannot tell where did I do wrong.