Question

PDE's: Solve the following PDE using separation of variables: 3u_x + 2u_y = 0, u(x,0) = 4e^(-x).

Answer 1

Please confirm, I got u(x,y) = 4e^(-x+y)

Answer 2

I am not getting a zero when I plug in your answer

Answer 3

you can check the answer by taking derivatives and seeing if it satifies the equation. Ux = -4e^(y-x) Uy=4e^(y-x) 3*-4e^(y-x)+2*4e^(y-x) = -4e(y-x), so that can't be right. The answer is 4e^(1.5y-x)

Answer 4

u(x,y)=X(x)Y(y)

u_x= X' Y

u_y= X Y'

3X' Y=-2 X Y'

\[\frac{-3}{2} \frac{X'}{X}=\frac{Y'}{Y}\]

\[\frac{-3}{2} \frac{X'}{X}=C\]
\[-3/2 log X =C x\]

\[X = e^{\frac{-(2 C x)}{3}}\]
\[\frac{Y'}{Y}=C\]
\[Log[Y]=Cy+D\]
\[Y= K e^{c y}\]

Answer 5

u(x,y)= \[Ke^{cy} e^{(-2/3) C x}\]
using condition
K=4
C= -3/2

u(x,y)= \[4 e^{3/2y} e^{ x}\]

Answer 6

sorry C= 3/2

Answer 7

oh okay i see what I did wrong. I made both coefficients of x and y as 1 instead of just one of them being 1 and the other 3/2. thanks.

Answer 8

(careless mistake sorry, lol)

Answer 9

are you taking PDE course?

Answer 10

almost. the course is 3/4 linear algebra and the last 1/4 is PDE's and Fourier Series

Answer 11

Fourier Series are the best

Answer 12

lol haha I could have taken the other alternative, which has the last 1/4 as more on vector calculus (Green's, stoke's and stuff). what would have been better for a computer engineering course? my current one or that other alternative?

Answer 13

I'm sorry I couldn't quite understand that. are not as differential, and linear algebra?

Answer 14

In my opinion as, Electrical Engineering student, (Green's, stoke's and stuff) are not as useful as differential, and linear algebra

Answer 15

oh alright, sorry. but yeah, I've seen terms like Fast Fourier Transform and signal optimization in my introductory engineering courses, so I kind of have an idea how the last 1/4 could apply to my major. linear algebra has some nice computer applications too like in search engines and stuff, i think? haha.

Answer 16

Yeah, but that's mainly Electrical Engineering material , not sure if Computer Engineering students have to take Signal processing?

Answer 17

the design of my major is closer to the side of electrical engineering than computer science in the spectrum, so yeah, I do have to take a course on signals and systems.

Answer 18

Signal processing is math intensive
Fourier, Laplace, ...

Answer 19

oh wow.. haha better ready myself for my junior year then

Answer 20

Taken physics already?

Answer 21

yeah I've already finished the freshman level general subjects in my community college

Answer 22

oh good, because it's killing me

Answer 23

haha which one are you in?

Answer 24

E&M

Answer 25

oh yeah that one almost killed me too. you can do it, it's easier than dealing with PDE's and fourier, at least for me lol

Answer 26

Where do you go to school?

Answer 27

Texas A&M