71.1.21 problem 37 (page 40)

Internal problem ID [19197]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 37 (page 40)
Date solved : Thursday, October 02, 2025 at 03:43:03 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.119 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 0.141 (sec). Leaf size: 12

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

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