89.9.10 problem 10

Internal problem ID [24490]
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 : 10
Date solved : Thursday, October 02, 2025 at 10:42:31 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 4 y^{2}+10 y x -4 y+8+x \left (2 x +2 y-1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 79

ode:=4*y(x)^2+10*x*y(x)-4*y(x)+8+x*(2*x+2*y(x)-1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-2 x^{3}+x^{2}-\sqrt {4 x^{6}-4 x^{5}-7 x^{4}-4 c_1}}{2 x^{2}} \\ y &= \frac {-2 x^{3}+x^{2}+\sqrt {4 x^{6}-4 x^{5}-7 x^{4}-4 c_1}}{2 x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.488 (sec). Leaf size: 101

ode=2*( 2*y[x]^2+5*x*y[x]-2*y[x]+4 )+x*( 2*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 {\sqrt {x^3} \sqrt {4 x^7-4 x^6-7 x^5+4 c_1 x}}{2 x^4}-x+\frac {1}{2}\\ y(x)&\to \frac {\sqrt {x^3} \sqrt {4 x^7-4 x^6-7 x^5+4 c_1 x}}{2 x^4}-x+\frac {1}{2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(2*x + 2*y(x) - 1)*Derivative(y(x), x) + 10*x*y(x) + 4*y(x)**2 - 4*y(x) + 8,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out