46.4.9 problem 9

Internal problem ID [7336]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.5. Bessel Functions Y(x). General Solution page 200
Problem number : 9
Date solved : Monday, January 27, 2025 at 02:50:37 PM
CAS classification : [_Lienard]

\begin{align*} x y^{\prime \prime }-5 y^{\prime }+y x&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 32

Order:=6; 
dsolve(x*diff(y(x),x$2)-5*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
 

\[ y = c_{1} x^{6} \left (1-\frac {1}{16} x^{2}+\frac {1}{640} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (-86400-10800 x^{2}-1350 x^{4}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 44

AsymptoticDSolveValue[x*D[y[x],{x,2}]-5*D[y[x],x]+x*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {x^4}{64}+\frac {x^2}{8}+1\right )+c_2 \left (\frac {x^{10}}{640}-\frac {x^8}{16}+x^6\right ) \]