88.5.1 problem 1

Internal problem ID [23975]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 35
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:48:23 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y y^{\prime }+x^{6}-2 y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 34

ode:=x*y(x)*diff(y(x),x)+x^6-2*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.402 (sec). Leaf size: 43

ode=x*y[x]*D[y[x],{x,1}]+x^6-2*y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {-x^6+c_1 x^4}\\ y(x)&\to \sqrt {-x^6+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**6 + x*y(x)*Derivative(y(x), x) - 2*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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