Internal problem ID [2504]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 2(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{x -2 y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.663 (sec). Leaf size: 13
dsolve([diff(y(x),x)=exp(x-2*y(x)),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left (-1+2 \,{\mathrm e}^{x}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.335 (sec). Leaf size: 17
DSolve[{y'[x]==Exp[x-2*y[x]],y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \log \left (2 e^x-1\right ) \\ \end{align*}