26.2.3 problem Differential equations with Linear Coefficients. Exercise 8.3, page 69

Internal problem ID [6922]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number : Differential equations with Linear Coefficients. Exercise 8.3, page 69
Date solved : Tuesday, September 30, 2025 at 04:05:52 PM
CAS classification : [_quadrature]

\begin{align*} x +y+1+\left (2 x +2 y+2\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=x+y(x)+1+(2*x+2*y(x)+2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -x -1 \\ y &= -\frac {x}{2}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 22

ode=(x+y[x]+1)+(2*x+2*y[x]+2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.129 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (2*x + 2*y(x) + 2)*Derivative(y(x), x) + y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} - \frac {x}{2}, \ y{\left (x \right )} = - x - 1\right ] \]