13.3.7 problem 15

Internal problem ID [3550]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.8, page 68
Problem number : 15
Date solved : Tuesday, September 30, 2025 at 06:42:38 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 13

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

\[ y = x \,{\mathrm e}^{-c_1 x +1} \]

✓ Mathematica. Time used: 0.141 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.491 (sec). Leaf size: 10

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

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