67.7.3 problem 3

Internal problem ID [16448]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 3
Date solved : Thursday, October 02, 2025 at 01:33:32 PM
CAS classification : [_separable]

\begin{align*} 4 y^{2}-x^{2} y^{2}+y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=4*y(x)^2-x^2*y(x)^2+diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {3}{x^{3}-3 c_1 -12 x} \]

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 25

ode=4*y[x]^2-x^2*y[x]^2+D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {3}{x^3-12 x+3 c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = - \frac {3}{C_{1} + x^{3} - 12 x} \]