43.22.5 problem 1(e)

Internal problem ID [9037]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 198
Problem number : 1(e)
Date solved : Tuesday, September 30, 2025 at 06:02:19 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

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

\begin{align*} y &= 0 \\ y &= c_1 x \\ \end{align*}

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to 0\\ y(x)&\to c_1 x\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 5

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

\[ y{\left (x \right )} = C_{1} x \]