4.4.2 | 就是愛看書
2022年8月8日—Therootsoftheindicialequationdeterminethetypeofbehaviorofthesolution.Thisamountstoconsideringthreedifferentcases.
Example (PageIndex{3})(x{2} y{prime prime}+x y{prime}+left(x{2}-1 ight) y=0 .)
This equation is similar to the last example, but it is the Bessel equation of order one. The indicial equation is given by
[0=r(r-1)+r-1=r{2}-1 onumber ]
The roots are (r_{1}=1, r_{2}=-1 .) In this case the roots differ by an integer, (r_{1}-r_{2}=2).
The first solution can be obtained using
[ egin{aligned} y(x) &=sum_{n=0}{infty} c_{n} x{n+1} \ y{prime}(x) &=sum_{n=0}{infty} c_{n}(n+1) x{n} \ y{prime prime}(x) &=sum_{n=0}{infty} c_{n}(n+1)(n) x{n-1} end{aligned} label{4.47} ]
Inserting these series into the differential equation, we have
Indicial Equations | 就是愛看書
Indicial Equation | 就是愛看書
提要120:Indicial 方程式的推導 | 就是愛看書
4.4.2 | 就是愛看書
Frobenius method | 就是愛看書
How to find indicial equation | 就是愛看書
Introduction to indicial equation for Frobenius Method | 就是愛看書
Solving Indicial equations | 就是愛看書
Examples to find indicial equation and their roots | 就是愛看書
Exponential Equations (Indicial Equations) | 就是愛看書
《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...