How to find indicial equation | 就是愛看書
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2017年10月29日—1Answer1...thentheindicialequationisr(r−1)+p0r+q0=0orr2−4r=0showsr=0andr=4.Inthiscase4−0∈Zsor=4givesasolutionandlet ...
![How to find indicial equation](https://i.imgur.com/y8QtHep.jpg)
$y+dfrac{3}{x(x-1)}y-dfrac{2}{x(x-1)}y=0$ then $p(x)=dfrac{3}{x(x-1)}$ and $q(x)=-dfrac{2}{x(x-1)}$. The equation has two regular singular points $x=0$ and $x=1$. For $x=0$ we see $$p_0=lim_{x o0}xp(x)=lim_{x o0}dfrac{3}{x-1}=-3$$ and $$q_0=lim_{x o0}x2q(x)=lim_{x o0}dfrac{-2x}{x-1}=0$$ then the indicial equation is $r(r-1)+p_0r+q_0=0$ or $r2-4r=0$ shows $r=0$ and $r=4$. In this case $4-0inmathbb{Z}$ so $r=4$ gives a solution and let $y=x4(a_0+a_1x+a_2x2+cdots)$ to find the answer. Do like this with point $x=1$.
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《工程數學講義》鼎文資訊 978-986-0720-73-0 (全套:平裝, 30公分)
《工程數學講義》好看嗎?作者鼎文師資群編由「鼎文資訊」出版,ISBN:978-986-0720-73-0(全套:平裝,30公分),以下為此書詳...