54.3.275 problem 1291

Internal problem ID [12570]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1291
Date solved : Friday, October 03, 2025 at 03:38:19 AM
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*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 50

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

\[ y = c_1 \operatorname {hypergeom}\left (\left [\frac {13}{12}-\frac {\sqrt {10}}{12}, \frac {13}{12}+\frac {\sqrt {10}}{12}\right ], \left [\frac {5}{6}\right ], x\right )+c_2 \,x^{{1}/{6}} \operatorname {hypergeom}\left (\left [\frac {5}{4}-\frac {\sqrt {10}}{12}, \frac {5}{4}+\frac {\sqrt {10}}{12}\right ], \left [\frac {7}{6}\right ], x\right ) \]

✓ Mathematica. Time used: 0.072 (sec). Leaf size: 82

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

\begin{align*} 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 ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(48*x*(x - 1)*Derivative(y(x), (x, 2)) + (152*x - 40)*Derivative(y(x), x) + 53*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False