50.22.11 problem 2(c)

Internal problem ID [8154]
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)
Date solved : Monday, January 27, 2025 at 03:44:55 PM
CAS classification : [_Lienard]

\begin{align*} x y^{\prime \prime }-4 y^{\prime }+y x&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.017 (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);
 

\[ y = c_{1} x^{5} \left (1-\frac {1}{14} x^{2}+\frac {1}{504} x^{4}-\frac {1}{33264} x^{6}+\operatorname {O}\left (x^{8}\right )\right )+c_{2} \left (2880+480 x^{2}+120 x^{4}-20 x^{6}+\operatorname {O}\left (x^{8}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 58

AsymptoticDSolveValue[x*D[y[x],{x,2}]-4*D[y[x],x]+x*y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_1 \left (-\frac {x^6}{144}+\frac {x^4}{24}+\frac {x^2}{6}+1\right )+c_2 \left (-\frac {x^{11}}{33264}+\frac {x^9}{504}-\frac {x^7}{14}+x^5\right ) \]