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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: [tex]{1 \over r}(rV)''=V''+(2/r)V' [/tex](that was easy, but next point (b) is not)

(b) Use equation from (a) to solve:

[tex] u''+{2 \over r}u'=1[/tex], 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:

[tex]\Delta u-u=|x|^2[/tex] where [tex]x \in [/tex]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"