Write down the Lagrange-Charpit equations for the equation

and use them to show that

For the first term, I attempted the folllowing

Cannot see any link from this to continue on....

Thanks

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- Feb 8th 2011, 10:38 PMbugatti79Another Charpit PDE
Write down the Lagrange-Charpit equations for the equation

and use them to show that

For the first term, I attempted the folllowing

Cannot see any link from this to continue on....

Thanks - Feb 9th 2011, 05:56 AMJester
Since and , then eliminating q, i.e.

- Feb 9th 2011, 09:52 AMbugatti79
- Feb 16th 2011, 02:10 PMbugatti79
The final part of this involves solving this non linear PDE

with IC's

I have attached my solution as far as determining x and y in terms of s and t. Just hoping some one could check my work before I proceed?

Thanks - Feb 16th 2011, 02:53 PMJester
You have made a mistake which has snowballed. You have

which you said However, what you really have is

and or

which has the solution which in turn gives

Using your IC you can determine and The rest of the problem goes similarly. - Feb 17th 2011, 11:34 AMbugatti79
- Feb 18th 2011, 03:49 AMJester
You made the same mistake in solving for and you did earlier. Find and the same way as and .

- Feb 18th 2011, 09:45 AMbugatti79
- Feb 18th 2011, 09:54 AMJester
What you have is good! Use your expressions for and (you know and already) and subs into

and equate terms involving and . This will more conditions on your functions and - Feb 18th 2011, 10:33 AMbugatti79
- Feb 18th 2011, 10:35 AMJester
Now subs your expressions for x and y into these.

- Feb 18th 2011, 10:46 AMbugatti79
- Feb 18th 2011, 12:32 PMJester
This is what I'd do. You have which you solved giving

.

From then and since you know and then

.

If you use your IC for and this will give and . - Feb 18th 2011, 01:09 PMbugatti79
- Feb 19th 2011, 04:25 AMJester
From post #13, when then and so

.

Solve for and and sub into and .