Help me with this...

ywel84

New member
Joined
Feb 12, 2007
Messages
1
Hello!!!
My English is poor because I'm from Poland.

I have 3 exercises from subject called: Mathematical Method In Physics.
Would you be so kind and help me to solve this:

1.
(a) Prove that: \(\displaystyle {1 \over r}(rV)''=V''+(2/r)V'\)(that was easy, but next point (b) is not)
(b) Use equation from (a) to solve:
\(\displaystyle u''+{2 \over r}u'=1\), where 1<r<2, u(1)=1, u(2)=2

2.
With witch k border problem:
-u''-u=ku on (0, 1), u'(0)=1=u'(1)
have solution?

3.
Find restricted solution of border problem:

\(\displaystyle \Delta u-u=|x|^2\) where \(\displaystyle x \in\)B1(0) tight in R^3
u(x)=1 when |x|=1, |x| is euklides length of vector.
Use spherical variables and find solution dependent on "r"
 
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