75.4.7 problem 52

Internal problem ID [16709]
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 : 52
Date solved : Tuesday, January 28, 2025 at 09:19:02 AM
CAS classification : [_quadrature]

\begin{align*} {\mathrm e}^{-y} y^{\prime }&=1 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 12

dsolve(exp(-y(x))*diff(y(x),x)=1,y(x), singsol=all)
 

\[ y = \ln \left (-\frac {1}{x +c_{1}}\right ) \]

✓ Solution by Mathematica

Time used: 0.077 (sec). Leaf size: 16

DSolve[Exp[-y[x]]*D[y[x],x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\log (-x-c_1) \]