→ rebe212296 :第五題我解出來了 06/09 15:22
推 yueayase :fundamental set of solution是n個線性獨立解 06/09 22:49
→ yueayase :所以wronskian 不為0 06/09 22:49
http://ycc.math.fju.edu.tw/t2012s/odes2012s/odes2012sf1.pdf
裡面的第三,四,五,八題不會解
課本也找不到解答
第四題(來源:
http://www.chegg.com/homework-help/elementary-differential-equations-and-boundary-value-problems-9th-edition-chapter-7.4-problem-3p-solution-9780470383346)
Let X(1)X(2)...X(n) are the solutions of homogeneous equation
x' = P(t)x
Then the Wroskian satisfies the equation
or
Integrating both sides: (C is arbitrary constant of integration)
Taking the exponential of both sides and rearranging:
W=c e^∫(P11+P22+..+Pnn)dt
Let X(1)X(2) be the set of fundamental solutions.
W1=C1e^∫(P11+P22+..+Pnn)dt
W2=C2e^∫(P11+P22+..+Pnn)dt C1C2不為0 (這一步看不懂)
Therefore:
&
where &
Dividing W1 by W2 we get:
Therefore: where is a constant (c2 ≠ 0)
第八題看不懂題目
跪求解答 謝謝
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※ 編輯: rebe212296 來自: 123.193.28.181 (06/09 13:36)
※ 編輯: rebe212296 來自: 123.193.28.181 (06/09 13:37)