81.1.26 problem 2-24

Internal problem ID [21471]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-24
Date solved : Thursday, October 02, 2025 at 07:39:15 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = c_1 \,{\mathrm e}^{\frac {\ln \left (x \right )^{2}}{2}} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to c_1 e^{\frac {\log ^2(x)}{2}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.159 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} e^{\frac {\log {\left (x \right )}^{2}}{2}} \]