10.13.4 problem 5

Internal problem ID [1364]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 5.2, Series Solutions Near an Ordinary Point, Part I. page 263
Problem number : 5
Date solved : Monday, January 27, 2025 at 04:56:11 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} \left (1-x \right ) y^{\prime \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: 54

Order:=6; 
dsolve((1-x)*diff(y(x),x$2)+y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {1}{2} x^{2}-\frac {1}{6} x^{3}-\frac {1}{24} x^{4}-\frac {1}{60} x^{5}\right ) y \left (0\right )+\left (x -\frac {1}{6} x^{3}-\frac {1}{12} x^{4}-\frac {1}{24} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 63

AsymptoticDSolveValue[(1-x)*D[y[x],{x,2}]+y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (-\frac {x^5}{24}-\frac {x^4}{12}-\frac {x^3}{6}+x\right )+c_1 \left (-\frac {x^5}{60}-\frac {x^4}{24}-\frac {x^3}{6}-\frac {x^2}{2}+1\right ) \]