Internal problem ID [2556]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-x \,{\mathrm e}^{-2 y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 12
dsolve([diff(y(x),x)=x*exp(-2*y(x)),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left (x^{2}+1\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.36 (sec). Leaf size: 15
DSolve[{y'[x]==x*Exp[-2*y[x]],y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \log \left (x^2+1\right ) \\ \end{align*}