73.7.39 problem 39

Internal problem ID [15197]
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
Date solved : Tuesday, January 28, 2025 at 07:41:49 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.463 (sec). Leaf size: 20

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

\[ y(x)\to \frac {\log \left (-\frac {x^2}{2}+c_1\right )}{x} \]