Internal problem ID [5688]
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(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=8; dsolve(x^3*(x-1)*diff(y(x),x$2)-2*(x-1)*diff(y(x),x)+3*x*y(x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.081 (sec). Leaf size: 108
AsymptoticDSolveValue[x^3*(x-1)*y''[x]-2*(x-1)*y'[x]+3*x*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 e^{-\frac {1}{x^2}} \left (\frac {1731 x^7}{320}-\frac {795 x^6}{128}-\frac {51 x^5}{40}+\frac {63 x^4}{32}+\frac {x^3}{2}-\frac {3 x^2}{4}+1\right ) x^3+c_1 \left (-\frac {51 x^7}{320}-\frac {19 x^6}{128}-\frac {9 x^5}{40}-\frac {9 x^4}{32}-\frac {x^3}{2}-\frac {3 x^2}{4}+1\right ) \]