23.1.460 problem 450

Internal problem ID [5067]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 450
Date solved : Tuesday, September 30, 2025 at 11:31:34 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (2+2 x -y\right ) y^{\prime }+3+6 x -3 y&=0 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 21

ode:=(2+2*x-y(x))*diff(y(x),x)+3+6*x-3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 2 x -\frac {3 \operatorname {LambertW}\left (-\frac {c_1 \,{\mathrm e}^{\frac {7}{3}+\frac {25 x}{3}}}{3}\right )}{5}+\frac {7}{5} \]

✓ Mathematica. Time used: 2.167 (sec). Leaf size: 41

ode=(2+2*x-y[x])*D[y[x],x]+3*(1+2*x-y[x])==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {3}{5} W\left (-e^{\frac {25 x}{3}-1+c_1}\right )+2 x+\frac {7}{5}\\ y(x)&\to 2 x+\frac {7}{5} \end{align*}

✓ Sympy. Time used: 2.269 (sec). Leaf size: 110

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x + (2*x - y(x) + 2)*Derivative(y(x), x) - 3*y(x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = 2 x - \frac {3 W\left (\frac {\sqrt [3]{C_{1} e^{25 x}} e^{\frac {7}{3}}}{3}\right )}{5} + \frac {7}{5}, \ y{\left (x \right )} = 2 x - \frac {3 W\left (\frac {\sqrt [3]{C_{1} e^{25 x}} \left (-1 + \sqrt {3} i\right ) e^{\frac {7}{3}}}{6}\right )}{5} + \frac {7}{5}, \ y{\left (x \right )} = 2 x - \frac {3 W\left (- \frac {\sqrt [3]{C_{1} e^{25 x}} \left (1 + \sqrt {3} i\right ) e^{\frac {7}{3}}}{6}\right )}{5} + \frac {7}{5}\right ] \]