43.21.5 problem 1(e)

Internal problem ID [9021]
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 190
Problem number : 1(e)
Date solved : Tuesday, September 30, 2025 at 06:01:34 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=x^{2} y^{2}-4 x^{2} \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 28

ode:=diff(y(x),x) = x^2*y(x)^2-4*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-2 \,{\mathrm e}^{\frac {4 x^{3}}{3}} c_1 -2}{-1+{\mathrm e}^{\frac {4 x^{3}}{3}} c_1} \]

✓ Mathematica. Time used: 0.133 (sec). Leaf size: 48

ode=D[y[x],x]==x^2*y[x]^2-4*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-2) (K[1]+2)}dK[1]\&\right ]\left [\frac {x^3}{3}+c_1\right ]\\ y(x)&\to -2\\ y(x)&\to 2 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*y(x)**2 + 4*x**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out