7.14.6 problem 6

Internal problem ID [431]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.2 (Series solution near ordinary points). Problems at page 216
Problem number : 6
Date solved : Monday, January 27, 2025 at 02:53:36 AM
CAS classification : [_Gegenbauer]

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 25

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

\[ y(x)\to c_2 \left (x^3+x\right )+c_1 \left (x^4+6 x^2+1\right ) \]