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

Internal problem ID [5787]
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 : Monday, January 27, 2025 at 01:18:00 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

\begin{align*} y \left (x \right ) &= -x -1 \\ y \left (x \right ) &= c_{1} -\frac {x}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 22

DSolve[(x+y[x]+1)+(2*x+2*y[x]+2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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