56.5.21 problem 21

Internal problem ID [8982]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 21
Date solved : Monday, January 27, 2025 at 05:26:12 PM
CAS classification : [_separable]

\begin{align*} x^{2} y^{\prime }+{\mathrm e}^{-y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x)+exp(-y(x))=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.433 (sec). Leaf size: 12

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

\[ y(x)\to \log \left (\frac {1}{x}+c_1\right ) \]