anyone here can help me with differential equations problem(s)

Question

jada · Answer

Find the second solution by the method of reduction of order
x^2(1-x^2)y''-x^3y'-2y=0,   y=[(1-x^2)^.5]/2

anonymous · Answer

I can try, no guarantees

anonymous · Answer

Are you sure that is x^2(1-x^2)?

jada · Answer

Great! I soved it but my answer got is very complicated. I am sure I made a mistake somewhere

jada · Answer

yes

anonymous · Answer

It'll take me a couple minutes to attempt it, hold on

anonymous · Answer

It looks like it will be nasty because of that square root

jada · Answer

I got V"[(1-x^2)^.5]/x+V'(-2-x^2)/[x^2(1-x^2)^.5]=0

jada · Answer

then n(x)=e^[(3/2)ln(x^2-1)-2lnx]

jada · Answer

can you help me with the next step. my mind went to sleep...

anonymous · Answer

I'm getting weird answers for the derivatives...

jada · Answer

ok skip that just help me rewrite the expression for n(x) if you can

anonymous · Answer

Just to be sure $$y=\sqrt{1-x ^{2}}/2$$?

jada · Answer

the orginal y?

anonymous · Answer

yes

jada · Answer

oh man  i posted wrong its over x instead of 2

anonymous · Answer

I see

jada · Answer

so sorry

anonymous · Answer

Everything else is right?

jada · Answer

yes

anonymous · Answer

n(x) which I assume is your integrating factor is going to be ((x^2-1)^(3/2))/x^2

jada · Answer

thank you.

jada · Answer

i actually realized i should use seperation of variables here, not integrating factor since the right side of equation equals 0