90.5.14 problem 14

Internal problem ID [25133]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 71
Problem number : 14
Date solved : Thursday, October 02, 2025 at 11:53:33 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\[ y^{{1}/{3}}-\frac {t}{4}-\frac {c_1}{t^{{1}/{3}}} = 0 \]

✓ Mathematica. Time used: 0.103 (sec). Leaf size: 24

ode=D[y[t],{t,1}] +y[t]/t == y[t]^(2/3); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {\left (t^{4/3}+4 c_1\right ){}^3}{64 t} \end{align*}

✓ Sympy. Time used: 0.148 (sec). Leaf size: 34

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

\[ y{\left (t \right )} = \frac {C_{1}^{3}}{t} + \frac {3 C_{1}^{2} \sqrt [3]{t}}{4} + \frac {3 C_{1} t^{\frac {5}{3}}}{16} + \frac {t^{3}}{64} \]