Internal problem ID [15004]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 4. Equations with variables separable and equations reducible to them. Exercises
page 38
Problem number: 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x +1\right ) y^{\prime }-y=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve((x+1)*diff(y(x),x)=y(x)-1,y(x), singsol=all)
\[ y = c_{1} x +c_{1} +1 \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 18
DSolve[(x+1)*y'[x]==y[x]-1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+c_1 (x+1) \\ y(x)\to 1 \\ \end{align*}