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 : Sunday, March 30, 2025 at 06:46:42 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 18

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

\[ y = -\frac {1}{2 \operatorname {LambertW}\left (-\frac {c_1}{2 x^{2}}\right ) x} \]

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

ode=x(1-2 x y[x])D[y[x],x]+(1+2 x y[x])y[x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.833 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(-2*x*y(x) + 1)*Derivative(y(x), x) + (2*x*y(x) + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x e^{C_{1} + W\left (- \frac {e^{- C_{1}}}{2 x^{2}}\right )} \]