50.20.7 problem 5

Internal problem ID [8135]
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 : Monday, January 27, 2025 at 03:44:30 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 38

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 42

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

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