Recent content by BrettJimison

Update: I found r to be 1+/- sqrt (5). think I'm good now..

The original equation is: 2x^2y''-xy'+(x^2+1)y=0 It's kind of a bear to solve. Basically after a bunch of work plugging in the y and its derivatives I need to combine two sums. One starts at x^0 and the other starts at x^2 so I have to pick off two terms from the first sum to combine them. The...

My confusion is this: the c1 and c2 are not necessarily equal to each other, so I can't just factor them out. Before I had indicial eqns of the form c1(r)(r-2)=0 or something similar and it's easy to see the roots are 0 and 2. Now I have two terms tied up with two different constants...

Homework Statement Hello all, I have a quick question, I'm solving a d.e using the Frobenius method and I have the indicial equation: C1(2r-1)(r-1)+C2x(r)(2r+1)=0 Where c1 and c2 are arbitrary constants not equal to zero. Homework EquationsThe Attempt at a Solution My question is, what are...

Ahhh! It's so easy! Thanks, for some reason I just couldn't get it...thanks a lot! It's been a while since I've thought about infinite series

Thanks for the response hallsofivy, I'm a little confused: the pattern is 6 , (6)(10) , (6)(10)(14) , (6)(10)(14)(18) , ... And yes it is also 2(3) , 2(3)*2(5) , 2(3)*2(5)*2(7) ect... But writing the General term as (2n+1)!/2^n(n)! Doesn't fit the pattern...

Homework Statement hello all, I'm in the middle of solving a d.e using the series method. I have come across a weird pattern in part of my solution that I'm confused about: 6, (6)(10),(6)(10)(14),(6)(10)(14)(18),... Homework EquationsThe Attempt at a Solution I can see its 2(3), 2(3)*2(5)...

Delta means this:in order to find your time for s2, you find the time it takes to fall a distance h under gravity with an initial velocity (in the y direction) of zero. This will give you the wrong time. You need to account for the initial vertical velocity. Think: which takes longer to hit the...

W(y1,y2,y3)(x)=0 Thanks for your time and help!

Ok Thanks for your time! If the Det wasnt zero, then equations would be linearly independent and ONLY the trivial solution would work. I can explain my reasoning in words, but I am having a hard time putting it into math... Thanks!

Sorry meant to say if the determinant WAS zero...typo, this is what I have been trying to prove the whole time.

The SPECIFIC question states: Suppose y1,y2,y3 are three distinct solutions of L2[y] =0 on I = (a,b) Show that W(y1,y2,y3)(x)=0 on I.

Im pretty sure cramers rule would just tell us we could find non trivial solutions...

If the determinant wasnt zero (wronskian) then that means that there is non trivial solutions to the system which means linear dependence but I don't know how to show that since I can't compute the wronskian to show that it isn't zero...

I actually get exactly what I posted previously...hmmm The thing is: I know the set of equations is L.D and I know the wronskian will be zero. I have no idea how to show its zero though. When I take the determinant of the matrix, I don't get something that cancells [edit] I understand why its...