Internal problem ID [13141]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 39.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(x+y(x)*exp(x*y(x))+x*exp(x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\ln \left (-\frac {x^{2}}{2}-c_{1} \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.412 (sec). Leaf size: 20
DSolve[x+y[x]*Exp[x*y[x]]+x*Exp[x*y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\log \left (-\frac {x^2}{2}+c_1\right )}{x} \]