54.3.100 problem 1114

Internal problem ID [12395]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1114
Date solved : Friday, October 03, 2025 at 03:18:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 36

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

\[ y = \left (c_2 \operatorname {BesselK}\left (0, -x \right )-c_2 \operatorname {BesselK}\left (1, -x \right )+c_1 \left (\operatorname {BesselI}\left (0, -x \right )+\operatorname {BesselI}\left (1, -x \right )\right )\right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.123 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to c_2 G_{1,2}^{2,0}\left (-2 x\left | \begin {array}{c} \frac {1}{2} \\ -1,0 \\ \end {array} \right .\right )+c_1 e^x (\operatorname {BesselI}(0,x)-\operatorname {BesselI}(1,x)) \end{align*}

✗ Sympy

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

False