60.3.311 problem 1317

Internal problem ID [11321]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1317
Date solved : Tuesday, January 28, 2025 at 05:59:19 PM
CAS classification : [[_elliptic, _class_I]]

\begin{align*} x \left (x^{2}-1\right ) y^{\prime \prime }+\left (3 x^{2}-1\right ) y^{\prime }+y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.149 (sec). Leaf size: 13

dsolve(x*(x^2-1)*diff(diff(y(x),x),x)+(3*x^2-1)*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.423 (sec). Leaf size: 38

DSolve[x*y[x] + (-1 + 3*x^2)*D[y[x],x] + x*(-1 + x^2)*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

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