63.1.129 problem 188

Internal problem ID [15569]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 188
Date solved : Thursday, October 02, 2025 at 10:20:07 AM
CAS classification : [_Bernoulli]

\begin{align*} x y^{\prime }-y^{2} \ln \left (x \right )+y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=x*diff(y(x),x)+y(x)-y(x)^2*ln(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{1+c_1 x +\ln \left (x \right )} \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 20

ode=x*D[y[x],x]+y[x]-y[x]^2*Log[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{\log (x)+c_1 x+1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.145 (sec). Leaf size: 12

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

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