Solve second order ode x*y''(x)+2*y'(x)=0 by trying y(x)=x^m?
回答 (1)
2016-05-15 8:47 am
✔ 最佳答案
Let z = y'Then y'' = z'
x*y'' + 2*y' = 0
x*z' + 2z = 0
Let z = x^m
Then z' = m*x^(m-1)
x*z' + 2z = x*m*x^(m-1) + 2*x^m = 0
m*x^m + 2*x^m = 0
( m + 2 ) * x^m = 0 , for all x
m = - 2
y' = z = x^(-2)
y = ∫ x^(-2) dx = - 1/x + c
Ans: y(x) = - 1/x + c
收錄日期: 2021-05-02 14:08:57
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160514205553AAcKb8n