80.2.2 problem 3

Internal problem ID [21145]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 2. Theory of first order differential equations. Excercise 2.6 at page 37
Problem number : 3
Date solved : Thursday, October 02, 2025 at 07:10:11 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=\frac {3 x^{{1}/{3}}}{2} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=a \\ \end{align*}

✓ Maple. Time used: 0.060 (sec). Leaf size: 11

ode:=diff(x(t),t) = 3/2*x(t)^(1/3); 
ic:=[x(0) = a]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = \left (t +a^{{2}/{3}}\right )^{{3}/{2}} \]

✓ Mathematica. Time used: 0.138 (sec). Leaf size: 16

ode=D[x[t],t]==3/2*x[t]^(1/3); 
ic={x[0]==a}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \left (a^{2/3}+t\right )^{3/2} \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
a = symbols("a") 
x = Function("x") 
ode = Eq(-3*x(t)**(1/3)/2 + Derivative(x(t), t),0) 
ics = {x(0): a} 
dsolve(ode,func=x(t),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants