14.1.26 problem Problem 34

Internal problem ID [3583]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 34
Date solved : Tuesday, September 30, 2025 at 06:47:47 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1}{x^{{2}/{3}}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

ode:=diff(y(x),x) = 1/x^(2/3); 
dsolve(ode,y(x), singsol=all);
 

\[ y = 3 x^{{1}/{3}}+c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 15

ode=D[y[x],x]==x^(-2/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 \sqrt [3]{x}+c_1 \end{align*}

✓ Sympy. Time used: 0.126 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = C_{1} + 3 \sqrt [3]{x} \]