74.3.2 problem 2

Internal problem ID [19832]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 29. Problems at page 81
Problem number : 2
Date solved : Thursday, October 02, 2025 at 04:45:02 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} 2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 34

ode:=2*x^2*y(x)+y(x)^3-x^3*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.112 (sec). Leaf size: 47

ode=2*x^2*y[x]+y[x]^3-x^3*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x^2}{\sqrt {-x^2+c_1}}\\ y(x)&\to \frac {x^2}{\sqrt {-x^2+c_1}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.453 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3*Derivative(y(x), x) + 2*x**2*y(x) + y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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