Internal problem ID [11752]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 20, Series solutions of second order linear equations. Exercises page
195
Problem number: 20.2 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Hermite]
\[ \boxed {y^{\prime \prime }-x y^{\prime }+y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (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);
\[ y \left (x \right ) = \left (1-\frac {1}{2} x^{2}-\frac {1}{24} x^{4}\right ) y \left (0\right )+x D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ 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}]
\[ y(x)\to c_1 \left (-\frac {x^4}{24}-\frac {x^2}{2}+1\right )+c_2 x \]