Internal problem ID [1962]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 8, page 34
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {y \,{\mathrm e}^{y x}+2 y x +\left (x \,{\mathrm e}^{y x}+x^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve((y(x)*exp(x*y(x))+2*x*y(x))+(x*exp(x*y(x))+x^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \frac {-\operatorname {LambertW}\left (\frac {{\mathrm e}^{-\frac {c_{1}}{x}}}{x}\right )-\frac {c_{1}}{x}}{x} \]
✓ Solution by Mathematica
Time used: 3.117 (sec). Leaf size: 28
DSolve[(y[x]*Exp[x*y[x]]+2*x*y[x])+(x*Exp[x*y[x]]+x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1-x W\left (\frac {e^{\frac {c_1}{x}}}{x}\right )}{x^2} \]