求解數學難

👨🏻‍🏫 學術台數學

[匿名]

2013-08-03 1:32 am

consider the question

X * Uxy - YUyy - Uy = 0

use new variables (V,W) defined by V=X, W=XY to transform it into the equation

Uvw = 0

Hence show that the general solution of the PDE is

u(X,Y) = F(x) + G(xy)

更新1:

find the solution which matches the boundary conditions u(x,0) = x^2 + 1 and u(1,y)=2e^-y

回答 (1)

用戶9112

2013-08-03 4:11 am

✔ 最佳答案

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圖片參考：http://imgcld.yimg.com/8/n/HA05107138/o/20130802201036.jpg

2013-08-02 20:56:51 補充：
u(x,y)=f(x)+g(xy)
u(x,0)=f(x)+g(0)=x^2+1=>f(x)=x^2+1-g(0)
u(1,y)=f(1)+g(y)=2e^(-y)=>g(y)=2e^(-y)-f(1)
Hence u(x,y)=f(x)+g(xy)=x^2+1-g(0)+2e^(-xy)-f(1)
u(x,0)=x^2+1-g(0)+2-f(1)=x^2+1
=>g(0)+f(1)=2
So u(x,y)=x^2+2e^(-xy)-1

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收錄日期: 2021-04-23 23:26:02
原文連結 [永久失效]:
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求解數學難