16.1.8 problem 3(b)

Internal problem ID [3410]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 3(b)
Date solved : Tuesday, March 04, 2025 at 04:37:54 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.13 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.150 (sec). Leaf size: 10

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

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