60.3.276 problem 1292

Internal problem ID [11272]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1292
Date solved : Sunday, March 30, 2025 at 08:04:39 PM
CAS classification : [_Jacobi, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 50 x \left (x -1\right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 31

ode:=50*x*(x-1)*diff(diff(y(x),x),x)+25*(2*x-1)*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \left (\sqrt {x}+\sqrt {x -1}\right )^{{4}/{5}}+c_2}{\left (\sqrt {x}+\sqrt {x -1}\right )^{{2}/{5}}} \]

✓ Mathematica. Time used: 0.174 (sec). Leaf size: 49

ode=-2*y[x] + 25*(-1 + 2*x)*D[y[x],x] + 50*(-1 + x)*x*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 \cosh \left (\frac {2}{5} \text {arctanh}\left (\frac {1}{\sqrt {\frac {x-1}{x}}}\right )\right )+i c_2 \sinh \left (\frac {2}{5} \text {arctanh}\left (\frac {1}{\sqrt {\frac {x-1}{x}}}\right )\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(50*x*(x - 1)*Derivative(y(x), (x, 2)) + (50*x - 25)*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False