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 : Tuesday, March 04, 2025 at 05:56:50 PM
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*}

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

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

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

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

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

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

✓ Sympy. Time used: 0.334 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*exp(-2*y(x)) + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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