49.15.1 problem 1(a)

Internal problem ID [7687]
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(a)
Date solved : Monday, January 27, 2025 at 03:09:51 PM
CAS classification : [_Hermite]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 27

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

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