57.1.66 problem 66

Internal problem ID [9050]
Book : First order enumerated odes
Section : section 1
Problem number : 66
Date solved : Monday, January 27, 2025 at 05:31:28 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 13

dsolve(diff(y(x),x)=exp(x+y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.820 (sec). Leaf size: 18

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

\[ y(x)\to -\log \left (-e^x-c_1\right ) \]