Internal problem ID [4912]
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: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+y^{\prime }+36 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 59
Order:=6; dsolve(x*diff(y(x),x$2)+diff(y(x),x)+36*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\ln \relax (x ) c_{2}+c_{1}\right ) \left (1-36 x +324 x^{2}-1296 x^{3}+2916 x^{4}-\frac {104976}{25} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (72 x -972 x^{2}+4752 x^{3}-12150 x^{4}+\frac {2396952}{125} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 93
AsymptoticDSolveValue[x*y''[x]+y'[x]+36*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {104976 x^5}{25}+2916 x^4-1296 x^3+324 x^2-36 x+1\right )+c_2 \left (\frac {2396952 x^5}{125}-12150 x^4+4752 x^3-972 x^2+\left (-\frac {104976 x^5}{25}+2916 x^4-1296 x^3+324 x^2-36 x+1\right ) \log (x)+72 x\right ) \]