29.20.29 problem 576

Internal problem ID [5170]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 576
Date solved : Monday, January 27, 2025 at 10:16:58 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 5.732 (sec). Leaf size: 37

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

\begin{align*} y(x)\to -\frac {1}{2 x W\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x^2}\right )} \\ y(x)\to 0 \\ \end{align*}