60.3.277 problem 1293

Internal problem ID [11273]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1293
Date solved : Sunday, March 30, 2025 at 08:04:41 PM
CAS classification : [_Jacobi]

\begin{align*} 144 x \left (x -1\right ) y^{\prime \prime }+\left (120 x -48\right ) y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 33

ode:=144*x*(x-1)*diff(diff(y(x),x),x)+(120*x-48)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\operatorname {LegendreQ}\left (-\frac {1}{2}, \frac {2}{3}, \sqrt {1-x}\right ) c_2 +\operatorname {LegendreP}\left (-\frac {1}{2}, \frac {2}{3}, \sqrt {1-x}\right ) c_1 \right ) x^{{1}/{3}} \]

✓ Mathematica. Time used: 0.35 (sec). Leaf size: 44

ode=y[x] + (-48 + 120*x)*D[y[x],x] + 144*(-1 + x)*x*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to (-1)^{2/3} c_2 x^{2/3} \operatorname {Hypergeometric2F1}\left (\frac {7}{12},\frac {7}{12},\frac {5}{3},x\right )+c_1 \operatorname {Hypergeometric2F1}\left (-\frac {1}{12},-\frac {1}{12},\frac {1}{3},x\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(144*x*(x - 1)*Derivative(y(x), (x, 2)) + (120*x - 48)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False