68.3.8 problem 8

Internal problem ID [17155]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 8
Date solved : Thursday, October 02, 2025 at 01:45:23 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=6 y^{{2}/{3}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 5

ode:=diff(y(t),t) = 6*y(t)^(2/3); 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

ode=D[y[t],t]==6*y[t]^(2/3); 
ic={y[1]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.115 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-6*y(t)**(2/3) + Derivative(y(t), t),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 8 t^{3} - 24 t^{2} + 24 t - 8 \]