50.3.19 problem 3(c)

Internal problem ID [7843]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 3(c)
Date solved : Sunday, March 30, 2025 at 12:29:32 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+y&=x y^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.142 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.192 (sec). Leaf size: 10

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

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