Internal problem ID [5744]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Problems for review and discovert.
(B) Challenge Problems . Page 194
Problem number: 1(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y=0} \end {gather*} With the expansion point for the power series method at \(x = \infty \).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 414
Order:=8; dsolve(9*(x-2)^2*(x-3)*diff(y(x),x$2)+6*x*(x-2)*diff(y(x),x)+16*y(x)=0,y(x),type='series',x=Infinity);
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 130
AsymptoticDSolveValue[9*(x-2)^2*(x-3)*y''[x]+6*x*(x-2)*y'[x]+16*y[x]==0,y[x],{x,Infinity,7}]
\[ y(x)\to c_2 \left (-\frac {13}{3 x^{2/3}}-\frac {251}{45 x^{5/3}}-\frac {7781}{810 x^{8/3}}-\frac {22151}{1215 x^{11/3}}-\frac {669229}{18225 x^{14/3}}-\frac {216463313}{2788425 x^{17/3}}-\frac {7179886604}{41826375 x^{20/3}}+\sqrt [3]{x}\right )+c_1 \left (-\frac {401483448544}{1336967775 x^7}-\frac {4666732192}{40514175 x^6}-\frac {822592}{18225 x^5}-\frac {285704}{15795 x^4}-\frac {3004}{405 x^3}-\frac {28}{9 x^2}-\frac {4}{3 x}+1\right ) \]