Internal problem ID [1882]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x +y-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 11
dsolve(x*diff(y(x),x)+y(x)=y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{x c_{1}+1} \]
✓ Solution by Mathematica
Time used: 0.224 (sec). Leaf size: 25
DSolve[x*y'[x]+y[x]==y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{1+e^{c_1} x} \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}