Recent content by pinkbabe02

That`s what I had originally also but when I redid it, I saw that in this case x0=1 so the summation has (x-1) instead of x. then for my final recurrence relation, i have...(i attached the file)

I didn`t even think about double factorials but yes my professor just went over them in class the other day. Using them I have... a2k=((-2)k\frac{(2k-1)!}{(2k)!})a0 and likewise... a2k+1=((-2)k\frac{(2k)!}{(2k-1)!})a1 so in power series form, I have... (i attached the file with the form...

This helps a lot. I think I am trying to combine the numbers and simplify too quickly instead of letting it go so I can find a pattern. a2k=(-2)k\frac{(2k+1)!}{(2k)!}

But don`t I need the solution in the form of a summation? this is where i am really struggling. I don`t understand how to do that

I found y1(x)=a0(1-x2+(3/2)x4-(5/2)x6...)+a1(x-(4/3)x3+(32/15)x5-(128/35)x7...)

I got what I believe to be the correct recurrence relation... an+2=\frac{-2(n+1)}{(n+2)}an could you help get me started in how to find the radii of convergence?

Yes I just double checked it again and that`s what the problem states.

Thanks for your help! Do you know where I went wrong though? I did the problem multiple times and I get the same recurrence relation everytime

Homework Statement (1+2x^2)y''+6xy'+2y=0 1. find the power series solutions of the equation near x0=0...show the recurrence relation for an, derive a formula for an in terms of a0 and a1, and show the solution in the form y=a0y1(x)+a1y2(x) 2.what is the lower bound for the radii convergence...

differential equation help! Homework Statement (1+2x-x^2)y''-6xy'-6y=0 find power series solution of the equation near x0=1 (a)show the recurrence relation for an, (b)derive a formula for an in terms of a0 and a1, and (c)show the solution in the form y=a0y1(x)+a1y2(x) Homework...