78.8.44 problem 44

Internal problem ID [18171]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 44
Date solved : Monday, March 31, 2025 at 05:21:01 PM
CAS classification : [_Bernoulli]

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

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

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

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

✓ Mathematica. Time used: 0.137 (sec). Leaf size: 20

ode=x * D[y[x],x] + y[x]== y[x]^2*Log[x]; 
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: 0.223 (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)
 

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