作者AAJJBurnett (叫我投手)
看板Grad-ProbAsk
標題[理工] 台聯大工數c
時間Mon Oct 17 21:23:05 2011
Solve the differential equation (x^2 -1)y"-6xy'+12y=0
by power series of the form y(x)=ΣCnx^n
1.Find the recurrence relation of Cn.答案應該是Cn+2=Cn(n-3)(n-4/(n+1)(n+2)?
2.Find the two linearly independent solutions.Write the first three nonzero
terms of each series if it is an infinite series.
3.Find the guaranteed radius of convergence.
請問2.3小題要如何算
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.114.206.124
→ sean456:第一題跟我一樣 10/17 21:55
→ sean456:第二題我算出來解是y(x)=Co(1+6X^2+X^4)+C1(X+X^3) 10/17 21:57
→ sean456:應該是從上面找兩個解就好了 10/17 21:57
→ sean456:第三題應該是 |X|<1 10/17 21:57
→ sean456:其實解出來就是剛好兩個獨立的解了 10/17 22:07
→ sean456:不過你題目的係數十二少打一個y唷= = 10/17 22:17
※ 編輯: AAJJBurnett 來自: 140.114.206.124 (10/17 22:21)