44.4.28 problem 10 (b)

Internal problem ID [7041]
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 (b)
Date solved : Monday, January 27, 2025 at 02:42:06 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&={\frac {5}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 21

dsolve([diff(y(x),x)=x*exp(y(x)),y(1) = 5/2],y(x), singsol=all)
 

\[ y = \ln \left (2\right )-\ln \left (-x^{2}+1+2 \,{\mathrm e}^{-\frac {5}{2}}\right ) \]

✓ Solution by Mathematica

Time used: 0.139 (sec). Leaf size: 24

DSolve[{D[y[x],x]==x*Exp[y[x]],{y[1]==25/10}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\log \left (-\frac {x^2}{2}+\frac {1}{e^{5/2}}+\frac {1}{2}\right ) \]