60.1.115 problem 118

Internal problem ID [10129]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 118
Date solved : Sunday, March 30, 2025 at 03:19:02 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 8

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

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

✓ Mathematica. Time used: 0.186 (sec). Leaf size: 18

ode=x*D[y[x],x] - y[x]*Log[y[x]]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to e^{e^{c_1} x} \\ y(x)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.272 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = e^{C_{1} x} \]