50.23.2 problem 1(b)

Internal problem ID [8165]
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)
Date solved : Monday, January 27, 2025 at 03:45:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 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{align*}

Using series method with expansion around

\begin{align*} \infty \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 96

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);
 

\[ y = \frac {c_{1} \left (1-\frac {13}{3 x}-\frac {251}{45 x^{2}}-\frac {7781}{810 x^{3}}-\frac {22151}{1215 x^{4}}-\frac {669229}{18225 x^{5}}-\frac {216463313}{2788425 x^{6}}-\frac {7179886604}{41826375 x^{7}}+O\left (\frac {1}{x^{8}}\right )\right )}{\left (\frac {1}{x}\right )^{{1}/{3}}}+c_{2} \left (1-\frac {4}{3 x}-\frac {28}{9 x^{2}}-\frac {3004}{405 x^{3}}-\frac {285704}{15795 x^{4}}-\frac {822592}{18225 x^{5}}-\frac {4666732192}{40514175 x^{6}}-\frac {401483448544}{1336967775 x^{7}}+O\left (\frac {1}{x^{8}}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 130

AsymptoticDSolveValue[9*(x-2)^2*(x-3)*D[y[x],{x,2}]+6*x*(x-2)*D[y[x],x]+16*y[x]==0,y[x],{x,Infinity,"8"-1}]
 

\[ y(x)\to c_2 \left (-\frac {13}{3 x^{2/3}}-\frac {251}{45 x^{5/3}}-\frac {7781}{810 x^{8/3}}-\frac {22151}{1215 x^{11/3}}-\frac {669229}{18225 x^{14/3}}-\frac {216463313}{2788425 x^{17/3}}-\frac {7179886604}{41826375 x^{20/3}}+\sqrt [3]{x}\right )+c_1 \left (-\frac {401483448544}{1336967775 x^7}-\frac {4666732192}{40514175 x^6}-\frac {822592}{18225 x^5}-\frac {285704}{15795 x^4}-\frac {3004}{405 x^3}-\frac {28}{9 x^2}-\frac {4}{3 x}+1\right ) \]