Internal problem ID [4909]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (36 x^{4}-16\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 31
Order:=6; dsolve(9*x^2*diff(y(x),x$2)+9*x*diff(y(x),x)+(36*x^4-16)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} x^{\frac {8}{3}} \left (1-\frac {3}{20} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{1} \left (1-\frac {3}{4} x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{\frac {4}{3}}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 38
AsymptoticDSolveValue[9*x^2*y''[x]+9*x*y'[x]+(36*x^4-16)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (1-\frac {3 x^4}{20}\right ) x^{4/3}+\frac {c_2 \left (1-\frac {3 x^4}{4}\right )}{x^{4/3}} \]