54.3.249 problem 1265

Internal problem ID [12544]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1265
Date solved : Friday, October 03, 2025 at 03:30:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -1\right ) \left (x -2\right ) y^{\prime \prime }-\left (2 x -3\right ) y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 94

ode:=(x-1)*(x-2)*diff(diff(y(x),x),x)-(2*x-3)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 57

ode=y[x] - (-3 + 2*x)*D[y[x],x] + (-2 + x)*(-1 + x)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \left (x^2-3 x+2\right ) \left (c_1 P_{\frac {1}{2} \left (-1+\sqrt {5}\right )}^2(2 x-3)+c_2 Q_{\frac {1}{2} \left (-1+\sqrt {5}\right )}^2(2 x-3)\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 2)*(x - 1)*Derivative(y(x), (x, 2)) - (2*x - 3)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False