60.3.294 problem 1300

Internal problem ID [11304]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1300
Date solved : Monday, January 27, 2025 at 11:10:53 PM
CAS classification : [_Gegenbauer]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 39

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

\[ y(x)\to a c_1 x-\frac {1}{2} c_2 (a x \log (1-a x)-a x \log (a x+1)+2) \]