67.1.6 problem Problem 1(f)

Internal problem ID [13874]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 2, First Order Equations. Problems page 149
Problem number : Problem 1(f)
Date solved : Wednesday, March 05, 2025 at 10:20:17 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (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: 0.137 (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: 0.187 (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)
 

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