Internal problem ID [12428]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y-\left (1-x \right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((1+y(x))-(1-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} -x}{-1+x} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 22
DSolve[(1+y[x])-(1-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x+c_1}{1-x} \\ y(x)\to -1 \\ \end{align*}