15.31 problem 439

Internal problem ID [3185]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 15
Problem number: 439.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class D], _rational, [_Abel, 2nd type, class A]]

Solve \begin {gather*} \boxed {\left (x -y\right ) y^{\prime }-y \left (2 y x +1\right )=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 18

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

\[ y \relax (x ) = -\frac {x}{\LambertW \left (-{\mathrm e}^{x^{2}} c_{1} x \right )} \]

Solution by Mathematica

Time used: 0.146 (sec). Leaf size: 24

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

\begin{align*} y(x)\to -\frac {x}{\text {ProductLog}\left (x \left (-e^{x^2-c_1}\right )\right )} \\ \end{align*}