60.1.75 problem 75

Internal problem ID [10089]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 75
Date solved : Monday, January 27, 2025 at 06:26:02 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.137 (sec). Leaf size: 20

dsolve(diff(y(x),x) - exp(x-y(x)) + exp(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 2.237 (sec). Leaf size: 23

DSolve[D[y[x],x] - Exp[x-y[x]] + Exp[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \log \left (1+e^{-e^x+c_1}\right ) \\ y(x)\to 0 \\ \end{align*}