67.3.37 problem 4.7 (k)

Internal problem ID [16358]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.7 (k)
Date solved : Thursday, October 02, 2025 at 01:22:25 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 27

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

\begin{align*} y &= \frac {1}{\sqrt {-3 x^{2}+c_1}} \\ y &= -\frac {1}{\sqrt {-3 x^{2}+c_1}} \\ \end{align*}

✓ Mathematica. Time used: 0.098 (sec). Leaf size: 44

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

\begin{align*} y(x)&\to -\frac {1}{\sqrt {-3 x^2-2 c_1}}\\ y(x)&\to \frac {1}{\sqrt {-3 x^2-2 c_1}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.199 (sec). Leaf size: 32

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

\[ \left [ y{\left (x \right )} = - \sqrt {- \frac {1}{C_{1} + 3 x^{2}}}, \ y{\left (x \right )} = \sqrt {- \frac {1}{C_{1} + 3 x^{2}}}\right ] \]