20.28.2 problem 2

Internal problem ID [4064]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 11, Series Solutions to Linear Differential Equations. Additional problems. Section 11.7. page 788
Problem number : 2
Date solved : Monday, January 27, 2025 at 08:07:22 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }-x^{2} y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 29

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

\[ y \left (x \right ) = \left (1+\frac {x^{4}}{12}\right ) y \left (0\right )+\left (x +\frac {1}{20} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 28

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

\[ y(x)\to c_2 \left (\frac {x^5}{20}+x\right )+c_1 \left (\frac {x^4}{12}+1\right ) \]