72.3.1 problem 1 (a)

Internal problem ID [19390]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 1 (a)
Date solved : Thursday, October 02, 2025 at 04:20:17 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2}-2 y^{2}+x y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

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

\begin{align*} y &= \sqrt {c_1 \,x^{2}+1}\, x \\ y &= -\sqrt {c_1 \,x^{2}+1}\, x \\ \end{align*}

✓ Mathematica. Time used: 0.38 (sec). Leaf size: 39

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

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

✓ Sympy. Time used: 0.242 (sec). Leaf size: 29

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

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