16.1.9 problem 3(c)

Internal problem ID [3411]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 3(c)
Date solved : Monday, January 27, 2025 at 07:35:58 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x)=-x*exp(y(x)),y(x), singsol=all)
 

\[ y \left (x \right ) = \ln \left (2\right )+\ln \left (\frac {1}{x^{2}+2 c_{1}}\right ) \]

✓ Solution by Mathematica

Time used: 0.297 (sec). Leaf size: 19

DSolve[D[y[x],x]==-x*Exp[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \log (2)-\log \left (x^2-2 c_1\right ) \]