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... ua-cam.com/video/aX8KDpI-q2A/v-deo.html, ua-cam.com/video/sM6YvEUiTp4/v-deo.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)
you're a lifesaver man, good vids
Thanks a lot for providing simple explanations for these cases.
explaint more about why you get x(0) =s, and y(0)=0?. thanks
For anyone confused, the last result on the page at 11:11 should read -1/5 outside the brackets rather than 1/5.
Brilliant!
you are good at mathematics. thanks
thanks, well explained
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... ua-cam.com/video/aX8KDpI-q2A/v-deo.html, ua-cam.com/video/sM6YvEUiTp4/v-deo.html
Thx alot my friend. What did you study if im allowed to ask? :=)
How about the 2nd-order ones? I know that at least the wave equation can be solved with characteristics.
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.
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.
find so difficult to understand how you get c(x) and the integration of each colorful terms
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!