### Author Topic: problem1 a (5)  (Read 1523 times)

#### Zhiman Tang

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##### problem1 a (5)
« on: January 18, 2019, 07:26:28 PM »
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.

« Last Edit: January 18, 2019, 09:10:22 PM by Victor Ivrii »