41.1.20 problem 20

Internal problem ID [8687]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 05:41:23 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\left (y-1\right ) \left (x +1\right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(x),x) = (y(x)-1)*(1+x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = 1+{\mathrm e}^{\frac {x \left (x +2\right )}{2}} c_1 \]

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 25

ode=D[y[x],x]==(y[x]-1)*(x+1); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 1+c_1 e^{\frac {1}{2} x (x+2)}\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.181 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x - 1)*(y(x) - 1) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x \left (\frac {x}{2} + 1\right )} + 1 \]