60.3.188 problem 1192

Internal problem ID [11198]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1192
Date solved : Monday, January 27, 2025 at 10:48:30 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.584 (sec). Leaf size: 51

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

\[ y = \left (\operatorname {HeunD}\left (4, 3, -8, 5, \frac {x -1}{x +1}\right ) {\mathrm e}^{-x} c_{1} +{\mathrm e}^{-\frac {1}{x}} \operatorname {HeunD}\left (-4, 3, -8, 5, \frac {x -1}{x +1}\right ) c_{2} \right ) \sqrt {x} \]

✓ Solution by Mathematica

Time used: 0.307 (sec). Leaf size: 35

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

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