59.1.474 problem 489

Internal problem ID [9646]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 489
Date solved : Monday, January 27, 2025 at 06:04:58 PM
CAS classification : [_Gegenbauer]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve((1-x^2)*diff(y(x),x$2)-8*x*diff(y(x),x)-12*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.314 (sec). Leaf size: 73

DSolve[(1-x^2)*D[y[x],{x,2}]-8*x*D[y[x],x]-12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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