71.1.69 problem 89 (page 123)

Internal problem ID [19245]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 89 (page 123)
Date solved : Thursday, October 02, 2025 at 03:51:29 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y \ln \left (y\right )^{2} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.133 (sec). Leaf size: 10

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

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