50.19.3 problem 1(c)

Internal problem ID [8111]
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. Section 4.4. REGULAR SINGULAR POINTS. Page 175
Problem number : 1(c)
Date solved : Monday, January 27, 2025 at 03:43:57 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime }&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✗ Solution by Maple

Order:=8; 
dsolve(x^2*diff(y(x),x$2)+(2-x)*diff(y(x),x)=0,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 64

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

\[ y(x)\to c_2 e^{2/x} \left (\frac {2835 x^7}{2}+315 x^6+\frac {315 x^5}{4}+\frac {45 x^4}{2}+\frac {15 x^3}{2}+3 x^2+\frac {3 x}{2}+1\right ) x^3+c_1 \]