44.5.1 problem 1(a)

Internal problem ID [9157]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 1(a)
Date solved : Tuesday, September 30, 2025 at 06:09:22 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: 0.378 (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: 0.235 (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)
 

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