14.1.21 problem Problem 29

Internal problem ID [3578]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 29
Date solved : Tuesday, September 30, 2025 at 06:46:03 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {1-y^{2}}{2+2 x y} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 21

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

\[ c_1 +\frac {1}{\left (y-1\right ) \left (x y+x +2\right )} = 0 \]

✓ Mathematica. Time used: 0.283 (sec). Leaf size: 58

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

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

✓ Sympy. Time used: 0.573 (sec). Leaf size: 36

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

\[ \left [ y{\left (x \right )} = \frac {- \sqrt {C_{1} x + x^{2} + 1} - 1}{x}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} x + x^{2} + 1} - 1}{x}\right ] \]