60.3.107 problem 1121

Internal problem ID [11103]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1121
Date solved : Wednesday, March 05, 2025 at 01:42:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

\[ y = \left (\left (\int \frac {{\mathrm e}^{\frac {x \left (x -2\right )}{2}}}{x^{2}}d x \right ) c_{1} +c_{2} \right ) x \]

✓ Mathematica. Time used: 0.319 (sec). Leaf size: 37

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

\[ y(x)\to x \left (c_2 \int _1^x\frac {e^{\frac {1}{2} (K[1]-2) K[1]}}{K[1]^2}dK[1]+c_1\right ) \]

✗ Sympy

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

False