60.3.108 problem 1122

Internal problem ID [11104]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1122
Date solved : Sunday, March 30, 2025 at 07:42:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.050 (sec). Leaf size: 28

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

\[ y = {\mathrm e}^{\frac {x^{2}}{2}} \left (c_2 \int \frac {{\mathrm e}^{-\frac {x \left (x +2\right )}{2}}}{x^{2}}d x +c_1 \right ) \]

✓ Mathematica. Time used: 0.338 (sec). Leaf size: 45

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

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

✗ Sympy

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

False