84.16.10 problem 8.19

Internal problem ID [22190]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 8. Linear first-order differential equations. Supplementary problems
Problem number : 8.19
Date solved : Thursday, October 02, 2025 at 08:33:50 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

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

\[ y = \frac {1}{1+{\mathrm e}^{x} c_1} \]

✓ Mathematica. Time used: 0.111 (sec). Leaf size: 25

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

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

✓ Sympy. Time used: 0.166 (sec). Leaf size: 8

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

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