23.1.484 problem 474

Internal problem ID [5091]
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 : 474
Date solved : Tuesday, September 30, 2025 at 11:34:56 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 23

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

\[ y = -\frac {2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {25 x}{4}-1-\frac {25 c_1}{4}}}{2}\right )}{5}+3 x -\frac {2}{5} \]

✓ Mathematica. Time used: 2.134 (sec). Leaf size: 40

ode=(6*x-2*y[x])*D[y[x],x]==2+3*x-y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 x-\frac {2}{5} \left (1+W\left (-e^{\frac {25 x}{4}-1+c_1}\right )\right )\\ y(x)&\to 3 x-\frac {2}{5} \end{align*}

✓ Sympy. Time used: 2.544 (sec). Leaf size: 122

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

\[ \left [ y{\left (x \right )} = 3 x - \frac {2 W\left (- \frac {\sqrt [4]{C_{1} e^{25 x}}}{2 e}\right )}{5} - \frac {2}{5}, \ y{\left (x \right )} = 3 x - \frac {2 W\left (\frac {\sqrt [4]{C_{1} e^{25 x}}}{2 e}\right )}{5} - \frac {2}{5}, \ y{\left (x \right )} = 3 x - \frac {2 W\left (- \frac {i \sqrt [4]{C_{1} e^{25 x}}}{2 e}\right )}{5} - \frac {2}{5}, \ y{\left (x \right )} = 3 x - \frac {2 W\left (\frac {i \sqrt [4]{C_{1} e^{25 x}}}{2 e}\right )}{5} - \frac {2}{5}\right ] \]