60.3.310 problem 1316

Internal problem ID [11320]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1316
Date solved : Tuesday, January 28, 2025 at 05:58:19 PM
CAS classification : [[_elliptic, _class_II]]

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

✓ Solution by Maple

Time used: 0.093 (sec). Leaf size: 18

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

\[ y = c_{1} \operatorname {EllipticE}\left (x \right )+c_{2} \left (\operatorname {EllipticCE}\left (x \right )-\operatorname {EllipticCK}\left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 15.062 (sec). Leaf size: 38

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

\[ y(x)\to c_2 G_{2,2}^{2,0}\left (x^2| \begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,0 \\ \end {array} \right )+\frac {2 c_1 \operatorname {EllipticE}\left (x^2\right )}{\pi } \]