Internal problem ID [1877]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x +1\right ) y^{\prime }-1+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 13
dsolve((1+x)*diff(y(x),x)-(1-y(x))=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}+x}{x +1} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 20
DSolve[(1+x)*y'[x]-(1-y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x+c_1}{x+1} \\ y(x)\to 1 \\ \end{align*}