23.1.495 problem 485

Internal problem ID [5102]
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 : 485
Date solved : Tuesday, September 30, 2025 at 11:37:15 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y&=0 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 23

ode:=(1+9*x-3*y(x))*diff(y(x),x)+2+3*x-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {LambertW}\left (3 \,{\mathrm e}^{-20 x -3+20 c_1}\right )}{6}+3 x +\frac {1}{2} \]

✓ Mathematica. Time used: 2.31 (sec). Leaf size: 37

ode=(1+9*x-3*y[x])*D[y[x],x]+2+3*x-y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{6} \left (W\left (-e^{-20 x-1+c_1}\right )+18 x+3\right )\\ y(x)&\to 3 x+\frac {1}{2} \end{align*}

✓ Sympy. Time used: 0.671 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x + (9*x - 3*y(x) + 1)*Derivative(y(x), x) - y(x) + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 x + \frac {W\left (C_{1} e^{- 20 x - 3}\right )}{6} + \frac {1}{2} \]