Internal problem ID [12679]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x \,{\mathrm e}^{y}+y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 15
dsolve([x*exp(y(x))+diff(y(x),x)=0,y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (2\right )-\ln \left (x^{2}+2\right ) \]
✓ Solution by Mathematica
Time used: 0.476 (sec). Leaf size: 16
DSolve[{x*Exp[y[x]]+y'[x]==0,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \log (2)-\log \left (x^2+2\right ) \]