58.2.11 problem 8

Internal problem ID [14552]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, section 1.3. Exercises page 22
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:38:42 AM
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: 0.013 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to \frac {2}{3} \sqrt {\frac {2}{3}} x^{3/2} \end{align*}

✓ Sympy. Time used: 0.497 (sec). Leaf size: 32

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

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