44.5.62 problem 52

Internal problem ID [7124]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 52
Date solved : Wednesday, March 05, 2025 at 04:15:17 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{{2}/{3}}-y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ -1-{\mathrm e}^{-\frac {x}{3}} c_1 +y^{{1}/{3}} = 0 \]

✓ Mathematica. Time used: 0.19 (sec). Leaf size: 39

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

\begin{align*} y(x)\to e^{-x} \left (e^{x/3}+e^{\frac {c_1}{3}}\right ){}^3 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.494 (sec). Leaf size: 32

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

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