89.9.1 problem 1

Internal problem ID [24481]
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 : 1
Date solved : Thursday, October 02, 2025 at 10:41:43 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 45

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

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

✓ Mathematica. Time used: 0.369 (sec). Leaf size: 76

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

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

✗ Sympy

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

Timed Out