Internal problem ID [5700]
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: 3(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 x y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 39
Order:=8; dsolve(x^3*diff(y(x),x$2)-4*x^2*diff(y(x),x)+3*x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = x^{\frac {5}{2}-\frac {\sqrt {13}}{2}} c_{1}+x^{\frac {5}{2}+\frac {\sqrt {13}}{2}} c_{2}+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 38
AsymptoticDSolveValue[x^3*y''[x]-4*x^2*y'[x]+3*x*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 x^{\frac {1}{2} \left (5+\sqrt {13}\right )}+c_2 x^{\frac {1}{2} \left (5-\sqrt {13}\right )} \]