15.1 problem 1(a)

Internal problem ID [5266]

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).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [_Hermite]

Solve \begin {gather*} \boxed {y^{\prime \prime }-x y^{\prime }+y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).

Solution by Maple

Time used: 0.002 (sec). Leaf size: 24

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

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

Solution by Mathematica

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

AsymptoticDSolveValue[y''[x]-x*y'[x]+y[x]==0,y[x],{x,0,5}]
 

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