60.3.241 problem 1246

Internal problem ID [11251]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1246
Date solved : Monday, January 27, 2025 at 11:00:32 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.116 (sec). Leaf size: 28

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

\[ y = \left (\operatorname {hypergeom}\left (\left [\frac {1}{2}, v +1\right ], \left [\frac {3}{2}\right ], x^{2}\right ) c_{2} x +c_{1} \right ) \left (x^{2}-1\right )^{v} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 32

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

\[ y(x)\to \left (x^2-1\right )^{v/2} (c_1 P_v^v(x)+c_2 Q_v^v(x)) \]