60.1.117 problem 120

Internal problem ID [10131]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 120
Date solved : Sunday, March 30, 2025 at 03:19:07 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Maple. Time used: 0.045 (sec). Leaf size: 16

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

\[ y = x^{2} {\mathrm e}^{-{\mathrm e}^{-x} c_1} \]

✓ Mathematica. Time used: 0.272 (sec). Leaf size: 20

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

\[ y(x)\to x^2 e^{-2 c_1 e^{-x}} \]

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (x*log(x**2/y(x)) + 2)*y(x)/x cannot be solved by the factorable group method