84.7.2 problem 4.2

Internal problem ID [22108]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 4. Separable first-order differential equations. Solved problems. Page 14
Problem number : 4.2
Date solved : Thursday, October 02, 2025 at 08:25:08 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ y = -\frac {4}{x^{4}-4 c_1} \]

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 22

ode=D[y[x],x]==y[x]^2*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {4}{x^4+4 c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = - \frac {4}{C_{1} + x^{4}} \]