Hi All,

I have 2 problems that I am stuck on (see attached), I dont know how to go any further. Any tips or advice on what Im doing wrong?

Thanks

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- Nov 24th 2010, 01:04 PMbugatti79Quasi Linear PDE's
Hi All,

I have 2 problems that I am stuck on (see attached), I dont know how to go any further. Any tips or advice on what Im doing wrong?

Thanks - Nov 24th 2010, 01:59 PMJester
You're not doing anything wrong - just not going far enough.

(1) You have

If you write it as

. It's Bernoulli in .

(2) You have

which integrates giving .

Then

or

.

This also integrates. - Nov 25th 2010, 09:08 AMbugatti79
- Nov 25th 2010, 09:21 AMJester
In part (1), multiply by 2x and let X = x^2 (it's linear now)

In (2) - looks good to me :-) - Nov 25th 2010, 09:33 AMbugatti79
- Nov 29th 2010, 07:11 AMbugatti79
- Nov 29th 2010, 02:58 PMJester
Multiplying by gives

and letting gives

or

. This is now linear! - Jan 17th 2011, 09:41 AMbugatti79
- Jan 17th 2011, 10:17 AMJester
First replace your with so your solution is

or

.

Are you sure about the IC b/c with , the only solution is . - Jan 17th 2011, 11:18 AMbugatti79
- Jan 17th 2011, 12:21 PMJester
As for your first question, it doesn't matter. Define

then drop the bar.

For your second question, let go back when we introduced new coordiantes such that

gave your PDE by choosing

with the IC as when From the second two we find

which integrates gives . Imposing the IC gives giving . - Jan 17th 2011, 12:54 PMbugatti79
- Jan 17th 2011, 02:35 PMJester
- Jan 17th 2011, 11:45 PMbugatti79
- Jan 18th 2011, 04:13 AMJester
For the general solution, it doesn't matter but for the IC , then it would matter.