75.4.32 problem 97

Internal problem ID [16734]
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
Date solved : Tuesday, January 28, 2025 at 09:20:04 AM
CAS classification : [_separable]

\begin{align*} \left (1+x \right ) y^{\prime }&=y-1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (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: 0.028 (sec). Leaf size: 18

DSolve[(x+1)*D[y[x],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*}