25.1.14 problem 14

Internal problem ID [4226]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 14
Date solved : Monday, January 27, 2025 at 08:43:01 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.070 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.329 (sec). Leaf size: 15

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

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