Homework Statement
L-1{(2s2+3)/(s2+3s-4)2}
The Attempt at a Solution
I factored the denominator
f(t)=(2s2+3)/((s-1)(s+4))2
now I've tried partial fractions to get
(2s2+3)/((s-1)(s+4))2 = A/(s-1)2 + B(s+4)2
(2s2+3)=A(s+4)2 + B(s-1)2
by substitution, s=1 and s=-4
5=A(25)
A=1/5
35=B(25)...
Homework Statement
Show that the Bessel functions Jn(x) (where n is an integer) have a very nice generating function, namely,
G(x,t) := ∑ from -∞ to ∞ of tn Jn(x) = exp {(x/2)((t-T1/t))},
Hint. Starting from the recurrence relation
Jn+1(x) + Jn-1(x) = (2n/x)Jn(x),
show that G(x,t)...
I'm not sure why the second half of my problem is in a subscript. The double checked the problem by previewing it, but I could get the text out of being in a subscript. My apologies for this.
Homework Statement
Starting from the recurrence relation, show that, when l is an integer, the polynomial solution to Legendre's equation is
yl(x) = Kl ∑ from k = 0 to (l/2) of (((-1)k) / k!) (((2l - 2k)!) / (l-k)! (l - 2k)!) (xl-2k)
where Kl is an arbitrary constant (depending on l) and x...
Hi Ehild,
My apologies for thinking I could use sec2x - 1. I thought the derivation was tanx from sec2x. I'll use sinx/cosx.
Thank you again for the help.
Homework Statement
(Reduction of order) The function y1 = x-1/2cosx is one solution to the differential equation x2y" + xy' + (x2 - 1/4) = 0. Use the method of reduction of order to find another linearly independent solution.
The Attempt at a Solution
I divided x2 to both sides to get the...
Thank you for the reply.
I retried by parts and saw that trig identities simplify the integrals, so I don't have to do by parts a second time. I apologize for not displaying my integrals.
My answer is y = c1sinx + c2cos +cosx
if you still want to see my work I can display it, but it's a lot...