40.3.22 problem 25 (g)

Internal problem ID [6626]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 25 (g)
Date solved : Sunday, March 30, 2025 at 11:12:46 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x y-2 y^{2}-\left (x^{2}-3 x y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 19

ode:=x*y(x)-2*y(x)^2-(x^2-3*x*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x}{3 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {c_1}{3}} x^{{1}/{3}}}{3}\right )} \]

✓ Mathematica. Time used: 4.571 (sec). Leaf size: 37

ode=(x*y[x]-2*y[x]^2)-(x^2-3*x*y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {x}{3 W\left (-\frac {1}{3} e^{-1-\frac {c_1}{3}} \sqrt [3]{x}\right )} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 14.407 (sec). Leaf size: 90

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x) - (x**2 - 3*x*y(x))*Derivative(y(x), x) - 2*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = x^{\frac {2}{3}} e^{C_{1} + W\left (\frac {\sqrt [3]{- x} \left (-1 + \sqrt {3} i\right ) e^{- C_{1}}}{6}\right )}, \ y{\left (x \right )} = x^{\frac {2}{3}} e^{C_{1} + W\left (\frac {\sqrt [3]{- x} \left (-1 - \sqrt {3} i\right ) e^{- C_{1}}}{6}\right )}, \ y{\left (x \right )} = x^{\frac {2}{3}} e^{C_{1} + W\left (\frac {\sqrt [3]{- x} e^{- C_{1}}}{3}\right )}\right ] \]