23.1.632 problem 626

Internal problem ID [5239]
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 : 626
Date solved : Tuesday, September 30, 2025 at 11:58:55 AM
CAS classification : [[_homogeneous, `class C`], _rational]

\begin{align*} \left (1-3 x -y\right )^{2} y^{\prime }&=\left (1-2 y\right ) \left (3-6 x -4 y\right ) \end{align*}

✓ Maple. Time used: 0.098 (sec). Leaf size: 75

ode:=(1-3*x-y(x))^2*diff(y(x),x) = (1-2*y(x))*(3-6*x-4*y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ 3 \ln \left (\frac {1-2 y}{6 x -1}\right )-4 \ln \left (2\right )-3 \ln \left (\frac {-y+3 x}{6 x -1}\right )-\ln \left (\frac {2-3 y-3 x}{6 x -1}\right )-\ln \left (6 x -1\right )-c_1 = 0 \]

✓ Mathematica. Time used: 60.113 (sec). Leaf size: 1089

ode=(1-3*x-y[x])^2* D[y[x],x]==(1-2*y[x])*(3-6*x-4*y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*y(x) - 1)*(-6*x - 4*y(x) + 3) + (-3*x - y(x) + 1)**2*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out