50.22.8 problem 1(h)

Internal problem ID [8151]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 4. Power Series Solutions and Special Functions. Problems for review and discovert. (A) Drill Exercises . Page 194
Problem number : 1(h)
Date solved : Monday, January 27, 2025 at 03:44:51 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x -1\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 79

Order:=8; 
dsolve((x-1)*diff(y(x),x$2)+(x+1)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1+\frac {1}{2} x^{2}+\frac {1}{3} x^{3}+\frac {3}{8} x^{4}+\frac {11}{30} x^{5}+\frac {53}{144} x^{6}+\frac {103}{280} x^{7}\right ) y \left (0\right )+\left (x +\frac {1}{2} x^{2}+\frac {2}{3} x^{3}+\frac {5}{8} x^{4}+\frac {19}{30} x^{5}+\frac {91}{144} x^{6}+\frac {177}{280} x^{7}\right ) y^{\prime }\left (0\right )+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 98

AsymptoticDSolveValue[(x-1)*D[y[x],{x,2}]+(x+1)*D[y[x],x]+y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_1 \left (\frac {103 x^7}{280}+\frac {53 x^6}{144}+\frac {11 x^5}{30}+\frac {3 x^4}{8}+\frac {x^3}{3}+\frac {x^2}{2}+1\right )+c_2 \left (\frac {177 x^7}{280}+\frac {91 x^6}{144}+\frac {19 x^5}{30}+\frac {5 x^4}{8}+\frac {2 x^3}{3}+\frac {x^2}{2}+x\right ) \]