1.8 problem 20

Internal problem ID [4787]

Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G. Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.1.2 page 230
Problem number: 20.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [_Hermite]

Solve \begin {gather*} \boxed {y^{\prime \prime }-x y^{\prime }+2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).

Solution by Maple

Time used: 0.016 (sec). Leaf size: 29

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

\[ y \relax (x ) = \left (-x^{2}+1\right ) y \relax (0)+\left (x -\frac {1}{6} x^{3}-\frac {1}{120} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]

Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 33

AsymptoticDSolveValue[y''[x]-x*y'[x]+2*y[x]==0,y[x],{x,0,5}]
 

\[ y(x)\to c_1 \left (1-x^2\right )+c_2 \left (-\frac {x^5}{120}-\frac {x^3}{6}+x\right ) \]