50.19.19 problem 6

Internal problem ID [8127]
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 : 6
Date solved : Monday, January 27, 2025 at 03:44:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \end{align*}

Using series method with expansion around

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

✗ Solution by Maple

Order:=8; 
dsolve(diff(y(x),x$2)+1/x^2*diff(y(x),x)-1/x^3*y(x)=0,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 17

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

\[ y(x)\to c_1 x+c_2 e^{\frac {1}{x}} x \]