71.6.9 problem 9

Internal problem ID [14415]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 06:30:14 AM
CAS classification : [_separable]

\begin{align*} x \,{\mathrm e}^{y}+y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.081 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.281 (sec). Leaf size: 16

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

\[ y(x)\to \log (2)-\log \left (x^2+2\right ) \]