5.15 problem 130

Internal problem ID [2879]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 5
Problem number: 130.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{x +y}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 13

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

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

Solution by Mathematica

Time used: 0.746 (sec). Leaf size: 18

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

\begin{align*} y(x)\to -\log \left (-e^x-c_1\right ) \\ \end{align*}