Internal problem ID [930]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x +y^{2}+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 11
dsolve(x*diff(y(x),x)+y(x)^2+y(x)= 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{x c_{1}-1} \]
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 27
DSolve[x*y'[x]+y[x]^2+y[x]== 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-1+e^{-c_1} x} \\ y(x)\to -1 \\ y(x)\to 0 \\ \end{align*}