Internal problem ID [3261]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 517.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {\left (y x +1\right ) y^{\prime }+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve((1+x*y(x))*diff(y(x),x)+y(x)^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\LambertW \left (x \,{\mathrm e}^{c_{1}}\right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 5.856 (sec). Leaf size: 21
DSolve[(1+x y[x])y'[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\text {ProductLog}\left (e^{c_1} x\right )}{x} \\ y(x)\to 0 \\ \end{align*}