78.1.7 problem 1 (h)

Internal problem ID [17991]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 1 (h)
Date solved : Monday, March 31, 2025 at 04:53:23 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Maple. Time used: 0.072 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.369 (sec). Leaf size: 93

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

\[ \text {Solve}\left [\frac {\sqrt {-\left (x^2 y(x)^2-1\right )^2}}{x (x y(x)-1)}-\frac {y(x) \sqrt {1-x^2 y(x)^2} \text {arcsinh}\left (x \sqrt {-y(x)^2}\right )}{\sqrt {-y(x)^2} \sqrt {x^2 y(x)^2-1}}=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out