44.4.27 problem 10 (a)

Internal problem ID [7040]
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 : Monday, January 27, 2025 at 02:42:03 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*}

✓ Solution by Maple

Time used: 0.054 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.257 (sec). Leaf size: 19

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

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