23.1.467 problem 457

Internal problem ID [5074]
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 : 457
Date solved : Tuesday, September 30, 2025 at 11:32:58 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.048 (sec). Leaf size: 196

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

\[ y = \frac {\frac {\left (1-i \sqrt {3}\right ) \left (12 c_1^{2} \sqrt {3}\, \left (x -1\right ) \sqrt {\frac {27 \left (x -1\right )^{2} c_1 -4 x +4}{c_1}}+8+108 c_1^{2} \left (x -1\right )^{2}+\left (-72 x +72\right ) c_1 \right )^{{2}/{3}}}{12}-\left (\frac {1}{3}+\left (-3+x \right ) c_1 \right ) \left (12 c_1^{2} \sqrt {3}\, \left (x -1\right ) \sqrt {\frac {27 \left (x -1\right )^{2} c_1 -4 x +4}{c_1}}+8+108 c_1^{2} \left (x -1\right )^{2}+\left (-72 x +72\right ) c_1 \right )^{{1}/{3}}+2 \left (-i \sqrt {3}-1\right ) \left (-\frac {1}{6}+\left (x -1\right ) c_1 \right )}{\left (12 c_1^{2} \sqrt {3}\, \left (x -1\right ) \sqrt {\frac {27 \left (x -1\right )^{2} c_1 -4 x +4}{c_1}}+8+108 c_1^{2} \left (x -1\right )^{2}+\left (-72 x +72\right ) c_1 \right )^{{1}/{3}} c_1} \]

✓ Mathematica. Time used: 60.064 (sec). Leaf size: 2581

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

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✗ Sympy

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

Timed Out