Internal problem ID [5706]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ 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: 0.041 (sec). Leaf size: 17
AsymptoticDSolveValue[y''[x]+1/x^2*y'[x]-1/x^3*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 x+c_2 e^{\frac {1}{x}} x \]