50.19.20 problem 8

Internal problem ID [8128]
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 : 8
Date solved : Monday, January 27, 2025 at 03:44:21 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=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)+(3*x-1)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 53

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

\[ y(x)\to c_1 \left (5040 x^7+720 x^6+120 x^5+24 x^4+6 x^3+2 x^2+x+1\right )+\frac {c_2 e^{-1/x}}{x} \]