At 7:34, I would recommend using the root method and the method of underdetermined coefficients instead. This lets you avoid doing all the annoying integration by parts.
@@raba2d723 I already did make a couple of videos about this. Here they are... th-cam.com/video/aX8KDpI-q2A/w-d-xo.html, th-cam.com/video/sM6YvEUiTp4/w-d-xo.html
you dont really say how this relates to the others... 1 you paramatize one you just know the slope... shouldn't this be called a different method all together?
i cannot solve the question. can u help me please? Given the linear equation: Ux-Uy=0 with the initial conditions: x(0,s)=0, y(0,s)=s, u(0,s)=g(s) where g(s) is an arbitrary differentiable function. a) Write the Characterist equations: a(x,y,u)Ux+b(x,y,u)Uy=c(x,y,u) dx = a(x,y,u) (1) dy = b(x,y,u) (2) du = c(x,y,u) (3) dt dt dt b) Integrate equations (1-2), use the initial conditions and determine x and y interms of the parameters t and s, then inverting these, write t and s interms of x and y. c) Integrate equations (3), use the initial conditions and determine u interms of t and s and then write u interms of x and y:u(x,y)
For anyone confused, the last result on the page at 11:11 should read -1/5 outside the brackets rather than 1/5.
explaint more about why you get x(0) =s, and y(0)=0?. thanks
At 7:34, I would recommend using the root method and the method of underdetermined coefficients instead. This lets you avoid doing all the annoying integration by parts.
make a video. im sure people appreciate that
@@raba2d723 I already did make a couple of videos about this. Here they are... th-cam.com/video/aX8KDpI-q2A/w-d-xo.html, th-cam.com/video/sM6YvEUiTp4/w-d-xo.html
Thank you very much, for that excellent step by step explanation
you're a lifesaver man, good vids
Thanks a lot for providing simple explanations for these cases.
amazing explanation
on 8:05 how and where did you get the integration? i got lost help p.z
How about the 2nd-order ones? I know that at least the wave equation can be solved with characteristics.
find so difficult to understand how you get c(x) and the integration of each colorful terms
you dont really say how this relates to the others... 1 you paramatize one you just know the slope... shouldn't this be called a different method all together?
It is the method of characteristic curves, but without a theory where these parameterizations come from, this solution cannot be understood much.
Brilliant!
you are good at mathematics. thanks
Thx alot my friend. What did you study if im allowed to ask? :=)
thanks, well explained
really happy for this!!
help me????
+Hung Dao why he get x(0)=s, y(0)=0?
@@daohung1112 Did you find out why he got that ? What I don't understand is why it is possible to arbitrarily set t=0 for the initial condition.
i cannot solve the question. can u help me please?
Given the linear equation: Ux-Uy=0 with the initial conditions: x(0,s)=0, y(0,s)=s, u(0,s)=g(s) where g(s) is an arbitrary differentiable function.
a) Write the Characterist equations: a(x,y,u)Ux+b(x,y,u)Uy=c(x,y,u)
dx = a(x,y,u) (1) dy = b(x,y,u) (2) du = c(x,y,u) (3)
dt dt dt
b) Integrate equations (1-2), use the initial conditions and determine x and y interms of the parameters t and s, then inverting these, write t and s interms of x and y.
c) Integrate equations (3), use the initial conditions and determine u interms of t and s and then write u interms of x and y:u(x,y)
help me, help me, help me please!