Internal problem ID [5733]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Problems for review and discovert.
(A) Drill Exercises . Page 194
Problem number: 2(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-4 y^{\prime }+x y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 36
Order:=8; dsolve(x*diff(y(x),x$2)-4*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{5} \left (1-\frac {1}{14} x^{2}+\frac {1}{504} x^{4}-\frac {1}{33264} x^{6}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} \left (2880+480 x^{2}+120 x^{4}-20 x^{6}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 58
AsymptoticDSolveValue[x*y''[x]-4*y'[x]+x*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (-\frac {x^6}{144}+\frac {x^4}{24}+\frac {x^2}{6}+1\right )+c_2 \left (-\frac {x^{11}}{33264}+\frac {x^9}{504}-\frac {x^7}{14}+x^5\right ) \]