29.5.14 problem 130

Internal problem ID [4731]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 130
Date solved : Monday, January 27, 2025 at 09:34:42 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.796 (sec). Leaf size: 18

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

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