89.8.3 problem 3

Internal problem ID [24463]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 66
Problem number : 3
Date solved : Thursday, October 02, 2025 at 10:39:15 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x -y+\left (4 x +y-6\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.096 (sec). Leaf size: 198

ode:=2*x-y(x)+(4*x+y(x)-6)*diff(y(x),x) = 0; 
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: 60.059 (sec). Leaf size: 2581

ode=( 2*x-y[x] )+(4*x+y[x]-6 )*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(2*x + (4*x + y(x) - 6)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out