89.5.7 problem 7

Internal problem ID [24357]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 7
Date solved : Thursday, October 02, 2025 at 10:21:44 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 34

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

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

✓ Mathematica. Time used: 60.08 (sec). Leaf size: 2353

ode=(y[x]-2)+(3*x-y[x])*D[y[x],x]== 0; 
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((3*x - y(x))*Derivative(y(x), x) + y(x) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out