54.3.98 problem 1112

Internal problem ID [12393]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1112
Date solved : Wednesday, October 01, 2025 at 01:44:18 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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

\[ y = c_1 \,{\mathrm e}^{2 x}+c_2 \,{\mathrm e}^{-x} \left (3 x +1\right ) \]

✓ Mathematica. Time used: 0.143 (sec). Leaf size: 37

ode=-2*(-1 + x)*y[x] - (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 e^{2 x+\frac {1}{2}} \left (c_2 \int _1^xe^{-3 K[1]} K[1]dK[1]+c_1\right ) \end{align*}

✗ Sympy

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

False