54.3.278 problem 1294

Internal problem ID [12573]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1294
Date solved : Friday, October 03, 2025 at 03:38:22 AM
CAS classification : [_Jacobi]

\begin{align*} 144 x \left (x -1\right ) y^{\prime \prime }+\left (168 x -96\right ) y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.031 (sec). Leaf size: 33

ode:=144*x*(x-1)*diff(diff(y(x),x),x)+(168*x-96)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\operatorname {LegendreQ}\left (-\frac {1}{2}, \frac {1}{3}, \sqrt {1-x}\right ) c_2 +\operatorname {LegendreP}\left (-\frac {1}{2}, \frac {1}{3}, \sqrt {1-x}\right ) c_1 \right ) x^{{1}/{6}} \]

✓ Mathematica. Time used: 0.066 (sec). Leaf size: 44

ode=y[x] + (-96 + 168*x)*D[y[x],x] + 144*(-1 + x)*x*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \operatorname {Hypergeometric2F1}\left (\frac {1}{12},\frac {1}{12},\frac {2}{3},x\right )+\sqrt [3]{-1} c_2 \sqrt [3]{x} \operatorname {Hypergeometric2F1}\left (\frac {5}{12},\frac {5}{12},\frac {4}{3},x\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(144*x*(x - 1)*Derivative(y(x), (x, 2)) + (168*x - 96)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False