59.1.222 problem 225

Internal problem ID [9394]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 225
Date solved : Monday, January 27, 2025 at 06:02:16 PM
CAS classification : [_Gegenbauer]

\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 48

dsolve((1-4*x^2)*diff(y(x),x$2)-20*x*diff(y(x),x)-16*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {2 \ln \left (2 x +\sqrt {4 x^{2}-1}\right ) c_{2} x +c_{1} x -\sqrt {4 x^{2}-1}\, c_{2}}{\left (4 x^{2}-1\right )^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.169 (sec). Leaf size: 57

DSolve[(1-4*x^2)*D[y[x],{x,2}]-20*x*D[y[x],x]-16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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