23.1.12 problem 2(b)

Internal problem ID [4102]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(b)
Date solved : Monday, January 27, 2025 at 08:08:49 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{x -2 y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 13

dsolve([diff(y(x),x)=exp(x-2*y(x)),y(0) = 0],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\ln \left (-1+2 \,{\mathrm e}^{x}\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.826 (sec). Leaf size: 17

DSolve[{D[y[x],x]==Exp[x-2*y[x]],y[0]==0},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \log \left (2 e^x-1\right ) \]