59.1.2 problem 2

Internal problem ID [9174]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 2
Date solved : Monday, January 27, 2025 at 05:51:43 PM
CAS classification : [_Gegenbauer]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 25

dsolve((x^2-1)*diff(y(x),x$2)-6*x*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
 

\[ y = c_{2} x^{4}+c_{1} x^{3}+6 c_{2} x^{2}+c_{1} x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.399 (sec). Leaf size: 75

DSolve[(x^2-1)*D[y[x],{x,2}]-6*x*D[y[x],x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (x^2-1\right )^{3/2} \exp \left (\int _1^x\frac {K[1]+4}{K[1]^2-1}dK[1]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[2]}\frac {K[1]+4}{K[1]^2-1}dK[1]\right )dK[2]+c_1\right ) \]