7.15.11 problem 11

Internal problem ID [467]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.3 (Regular singular points). Problems at page 231
Problem number : 11
Date solved : Monday, January 27, 2025 at 02:53:57 AM
CAS classification : [_Gegenbauer]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 34

Order:=6; 
dsolve((1-x^2)*diff(y(x),x$2)-(2*x)*diff(y(x),x)+12*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (3 x^{4}-6 x^{2}+1\right ) y \left (0\right )+\left (-\frac {5}{3} x^{3}+x \right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 31

AsymptoticDSolveValue[(1-x^2)*D[y[x],{x,2}]-(2*x)*D[y[x],x]+12*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (x-\frac {5 x^3}{3}\right )+c_1 \left (3 x^4-6 x^2+1\right ) \]