25.1.2 problem 2

Internal problem ID [4214]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 2
Date solved : Tuesday, March 04, 2025 at 05:56:19 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=6 x y^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=diff(y(x),x) = 6*x*y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.114 (sec). Leaf size: 22

ode=D[y[x],x]==6*x*y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.142 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x*y(x)**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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