10.14.12 problem 8

Internal problem ID [1394]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 5.3, Series Solutions Near an Ordinary Point, Part II. page 269
Problem number : 8
Date solved : Monday, January 27, 2025 at 04:56:40 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x y^{\prime \prime }+y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 69

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

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

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 78

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

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