76.3.13 problem 13

Internal problem ID [17313]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
Problem number : 13
Date solved : Monday, March 31, 2025 at 03:51:58 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{{1}/{3}} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 21

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

\[ y(t)\to \frac {2}{3} \sqrt {\frac {2}{3}} t^{3/2} \]

✓ Sympy. Time used: 0.709 (sec). Leaf size: 32

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

\[ \left [ y{\left (t \right )} = - \frac {2 \sqrt {6} t^{\frac {3}{2}}}{9}, \ y{\left (t \right )} = \frac {2 \sqrt {6} t^{\frac {3}{2}}}{9}\right ] \]