29.19.4 problem 517

Internal problem ID [5113]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 517
Date solved : Monday, January 27, 2025 at 10:12:04 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (1+y x \right ) y^{\prime }+y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 13

dsolve((1+x*y(x))*diff(y(x),x)+y(x)^2 = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\operatorname {LambertW}\left (x \,{\mathrm e}^{c_{1}}\right )}{x} \]

✓ Solution by Mathematica

Time used: 1.560 (sec). Leaf size: 21

DSolve[(1+x y[x])D[y[x],x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {W\left (e^{c_1} x\right )}{x} \\ y(x)\to 0 \\ \end{align*}