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Messages - Zhiman Tang

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Home Assignment 2 / problem4 (20)
« on: January 18, 2019, 11:53:36 PM »
the expression on the right hand contains both x and y,
the characteristic line is 3x-y=c
then, we evaluate du = xydx. in this step, we have to replace y by 3x-c before integrating both sides.
My question is, why we have to do so?
And after integrte both sides, why we have to replace c back by 3x-y?

Home Assignment 2 / Re: Home Assignment 2 Problem 2(a)
« on: January 18, 2019, 09:17:57 PM »
I think you need to find the value of u(0,0), below is my answer, but idk whether it is correct or not.
consider u(x,y) = f(x/y)
in this case, x=0 is not a problem, but y=0 is a problem
we can write u(0,y) = f(0),
to make u a contiunuos solution, we need u(0,0)=f(0) since the value of u can't jump at y=0
so u(0,0)=f(0) is the condition to make it continuos.

Home Assignment 2 / 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.

Home Assignment 1 / problem 4 (25)
« on: January 18, 2019, 07:01:19 PM »
uxy = uxuy
I use the hint and divide both sides by ux. I get ux = eu * f(x). I am stuck there. Could anybody help me out?

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