67.3.39 problem 4.7 (m)

Internal problem ID [16360]
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 (m)
Date solved : Thursday, October 02, 2025 at 01:22:31 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

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

\[ y = -\tanh \left (x^{3}+3 c_1 \right ) \]

✓ Mathematica. Time used: 0.138 (sec). Leaf size: 44

ode=D[y[x],x]-3*x^2*y[x]^2==-3*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]-1) (K[1]+1)}dK[1]\&\right ]\left [x^3+c_1\right ]\\ y(x)&\to -1\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.696 (sec). Leaf size: 12

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

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