50.19.13 problem 3(d)

Internal problem ID [8121]
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)
Date solved : Monday, January 27, 2025 at 03:44:12 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 y x&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 32

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);
 

\[ y = x^{{5}/{2}} \left (x^{-\frac {\sqrt {13}}{2}} c_{1} +x^{\frac {\sqrt {13}}{2}} c_{2} \right )+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 38

AsymptoticDSolveValue[x^3*D[y[x],{x,2}]-4*x^2*D[y[x],x]+3*x*y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_1 x^{\frac {1}{2} \left (5+\sqrt {13}\right )}+c_2 x^{\frac {1}{2} \left (5-\sqrt {13}\right )} \]