60.3.286 problem 1291

Internal problem ID [11296]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1291
Date solved : Tuesday, January 28, 2025 at 05:57:58 PM
CAS classification : [_Jacobi]

\begin{align*} 48 x \left (x -1\right ) y^{\prime \prime }+\left (152 x -40\right ) y^{\prime }+53 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.228 (sec). Leaf size: 50

dsolve(48*x*(x-1)*diff(diff(y(x),x),x)+(152*x-40)*diff(y(x),x)+53*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {hypergeom}\left (\left [\frac {13}{12}-\frac {\sqrt {10}}{12}, \frac {13}{12}+\frac {\sqrt {10}}{12}\right ], \left [\frac {5}{6}\right ], x\right )+c_{2} x^{{1}/{6}} \operatorname {hypergeom}\left (\left [\frac {5}{4}-\frac {\sqrt {10}}{12}, \frac {5}{4}+\frac {\sqrt {10}}{12}\right ], \left [\frac {7}{6}\right ], x\right ) \]

✓ Solution by Mathematica

Time used: 0.112 (sec). Leaf size: 82

DSolve[53*y[x] + (-40 + 152*x)*D[y[x],x] + 48*(-1 + x)*x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt [6]{-1} c_2 \sqrt [6]{x} \operatorname {Hypergeometric2F1}\left (\frac {5}{4}-\frac {\sqrt {\frac {5}{2}}}{6},\frac {1}{12} \left (15+\sqrt {10}\right ),\frac {7}{6},x\right )+c_1 \operatorname {Hypergeometric2F1}\left (\frac {1}{12} \left (13-\sqrt {10}\right ),\frac {1}{12} \left (13+\sqrt {10}\right ),\frac {5}{6},x\right ) \]