5.21 problem 21

Internal problem ID [6561]

Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 21.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {x^{2} y^{\prime }+{\mathrm e}^{-y}=0} \end {gather*}

Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

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

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

Solution by Mathematica

Time used: 0.362 (sec). Leaf size: 12

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

\begin{align*} y(x)\to \log \left (\frac {1}{x}+c_1\right ) \\ \end{align*}