44.20.7 problem 5

Internal problem ID [9421]
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 4.5. More on Regular Singular Points. Page 183
Problem number : 5
Date solved : Tuesday, September 30, 2025 at 06:18:34 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 \left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \end{align*}

Using series method with expansion around

\begin{align*} -1 \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 38

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

\[ y = \left (x +1\right )^{{2}/{3}} \left (\left (x +1\right )^{-\frac {\sqrt {7}}{3}} c_1 +\left (x +1\right )^{\frac {\sqrt {7}}{3}} c_2 \right )+O\left (x^{8}\right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 42

ode=3*(x+1)^2*D[y[x],{x,2}]-(x+1)*D[y[x],x]-y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,-1,7}]
 

\[ y(x)\to c_1 (x+1)^{\frac {1}{3} \left (2+\sqrt {7}\right )}+c_2 (x+1)^{\frac {1}{3} \left (2-\sqrt {7}\right )} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*(x + 1)**2*Derivative(y(x), (x, 2)) - (x + 1)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=-1,n=8)
 

IndexError : list index out of range