8.2.11 problem 13

Internal problem ID [671]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.3. Slope fields and solution curves. Page 26
Problem number : 13
Date solved : Saturday, March 29, 2025 at 10:12:09 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.087 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 23

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

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

✗ Sympy

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

NotImplementedError : Initial conditions produced too many solutions for constants