89.1.24 problem 24

Internal problem ID [24259]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 21
Problem number : 24
Date solved : Thursday, October 02, 2025 at 10:02:15 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.067 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.127 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.182 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(exp(3*x) + 1)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} e^{x}}{\sqrt [3]{e^{3 x} + 1}} \]