35.9.9 problem 5, using series method

Internal problem ID [6244]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 5, using series method
Date solved : Monday, January 27, 2025 at 01:49:56 PM
CAS classification : [[_2nd_order, _missing_x]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 39

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

\[ y = \left (1+\frac {1}{2} x^{2}+\frac {1}{24} x^{4}\right ) y \left (0\right )+\left (x +\frac {1}{6} x^{3}+\frac {1}{120} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 42

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

\[ y(x)\to c_2 \left (\frac {x^5}{120}+\frac {x^3}{6}+x\right )+c_1 \left (\frac {x^4}{24}+\frac {x^2}{2}+1\right ) \]