38.4.27 problem 10 (a)

Internal problem ID [8326]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 10 (a)
Date solved : Tuesday, September 30, 2025 at 05:26:35 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.114 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.197 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to -\log \left (e^2-\frac {x^2}{2}\right ) \end{align*}

✓ Sympy. Time used: 0.117 (sec). Leaf size: 19

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

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