36.1.31 problem 29 part(a)

Internal problem ID [6286]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 29 part(a)
Date solved : Sunday, March 30, 2025 at 10:49:11 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y^{{2}/{3}}-\frac {2 x}{3}-c_1 = 0 \]

✓ Mathematica. Time used: 0.175 (sec). Leaf size: 29

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

\begin{align*} y(x)\to \frac {2}{3} \sqrt {\frac {2}{3}} (x+c_1){}^{3/2} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.684 (sec). Leaf size: 36

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

\[ \left [ y{\left (x \right )} = - \frac {2 \sqrt {6} \left (C_{1} + x\right )^{\frac {3}{2}}}{9}, \ y{\left (x \right )} = \frac {2 \sqrt {6} \left (C_{1} + x\right )^{\frac {3}{2}}}{9}\right ] \]