Internal problem ID [4914]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+k^{2} x^{4} y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 14
Order:=6; dsolve(diff(y(x),x$2)+k^2*x^4*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = y \relax (0)+D\relax (y )\relax (0) x +O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 10
AsymptoticDSolveValue[y''[x]+k^2*x^4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 x+c_1 \]