49.15.3 problem 1(c)

Internal problem ID [7689]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 3. Linear equations with variable coefficients. Page 130
Problem number : 1(c)
Date solved : Monday, January 27, 2025 at 03:09:52 PM
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);
 

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

✓ 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}]
 

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