Internal problem ID [4908]
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: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+5 y^{\prime }+x y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 44
Order:=6; dsolve(x*diff(y(x),x$2)+5*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{4} \left (1-\frac {1}{12} x^{2}+\frac {1}{384} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \relax (x ) \left (9 x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\left (-144-36 x^{2}+\mathrm {O}\left (x^{6}\right )\right )\right )}{x^{4}} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 47
AsymptoticDSolveValue[x*y''[x]+5*y'[x]+x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^4}{384}-\frac {x^2}{12}+1\right )+c_1 \left (\frac {\left (x^2+8\right )^2}{64 x^4}-\frac {\log (x)}{16}\right ) \]