Another partial differential equation problem

  • Thread starter pentazoid
  • Start date
  • #1
146
0

Homework Statement



Derived the general solution of the given equation by using an appropriate change of variables
5.) du/dt-2(du/dx)=2

Homework Equations



du/dx=du/d(alpha)*d(alpha)/dx+du/d(beta)*d(beta)/dx
du/dt= du/d(alpha)*d(alpha)/dt+du/d(beta)*d(beta)/dt

The Attempt at a Solution



not really sure how to determine du/d(alpha),d(alpha)/dx,d(beta)/dx ,d(alpha)/dt,d(beta)/dt

book says alpha=x+2t, beta=x
 

Answers and Replies

  • #2
28
0

Homework Statement



Derived the general solution of the given equation by using an appropriate change of variables
5.) du/dt-2(du/dx)=2

Homework Equations



du/dx=du/d(alpha)*d(alpha)/dx+du/d(beta)*d(beta)/dx
du/dt= du/d(alpha)*d(alpha)/dt+du/d(beta)*d(beta)/dt

The Attempt at a Solution



not really sure how to determine du/d(alpha),d(alpha)/dx,d(beta)/dx ,d(alpha)/dt,d(beta)/dt

book says alpha=x+2t, beta=x
[tex]
\frac{\partial\alpha}{\partial x}=1,\frac{\partial\beta}{\partial x}=1 so
\[
\frac{\partial u}{\partial x}=\frac{\partial u}{\partial\alpha}\frac{\partial\alpha}{\partial x}+\frac{\partial u}{\partial\beta}\frac{\partial\beta}
{\partial x}=\frac{\partialu}{\partialx}=\frac{\partial u}{\partial\alpha}+\frac{\partial u}{\partial\beta}
\]
[/tex]
did that help?
 
  • #3
146
0
[tex]
\frac{\partial\alpha}{\partial x}=1,\frac{\partial\beta}{\partial x}=1 so
\[
\frac{\partial u}{\partial x}=\frac{\partial u}{\partial\alpha}\frac{\partial\alpha}{\partial x}+\frac{\partial u}{\partial\beta}\frac{\partial\beta}
{\partial x}=\frac{\partialu}{\partialx}=\frac{\partial u}{\partial\alpha}+\frac{\partial u}{\partial\beta}
\]
[/tex]
did that help?

I probably should have said in the back of the book, they give you alpha and beta. They don't give you the equations for alpha and beta in the problem. I don't understand how to determine alpha and beta.
 

Related Threads on Another partial differential equation problem

  • Last Post
Replies
1
Views
1K
Replies
7
Views
2K
  • Last Post
Replies
5
Views
987
  • Last Post
Replies
0
Views
844
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
1
Views
632
  • Last Post
Replies
2
Views
809
  • Last Post
Replies
5
Views
908
Replies
2
Views
511
Top