85.31.1 problem 5

Internal problem ID [22621]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 64
Problem number : 5
Date solved : Thursday, October 02, 2025 at 08:55:13 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 14

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

\[ y^{{1}/{3}}-x -c_1 = 0 \]

✓ Mathematica. Time used: 0.064 (sec). Leaf size: 22

ode=D[y[x],{x,1}]==3*y[x]^(2/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{27} (3 x+c_1){}^3\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = \frac {C_{1}^{3}}{27} + \frac {C_{1}^{2} x}{3} + C_{1} x^{2} + x^{3} \]