89.9.6 problem 6

Internal problem ID [24486]
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 72
Problem number : 6
Date solved : Thursday, October 02, 2025 at 10:42:21 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 2 y^{2}+3 y x -2 y+6 x +x \left (x +2 y-1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 67

ode:=2*y(x)^2+3*x*y(x)-2*y(x)+6*x+x*(x+2*y(x)-1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-x^{2}+x -\sqrt {x^{4}-10 x^{3}+x^{2}-4 c_1}}{2 x} \\ y &= \frac {-x^{2}+x +\sqrt {x^{4}-10 x^{3}+x^{2}-4 c_1}}{2 x} \\ \end{align*}

✓ Mathematica. Time used: 0.363 (sec). Leaf size: 82

ode=(2*y[x]^2+3*x*y[x]-2*y[x]+6*x)+x*( x+2*y[x]-1 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \left (-\frac {\sqrt {x^5-10 x^4+x^3+4 c_1 x}}{x^{3/2}}-x+1\right )\\ y(x)&\to \frac {1}{2} \left (\frac {\sqrt {x^5-10 x^4+x^3+4 c_1 x}}{x^{3/2}}-x+1\right ) \end{align*}

✗ Sympy

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

Timed Out