66.1.11 problem 14

Internal problem ID [15898]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.2. page 33
Problem number : 14
Date solved : Thursday, October 02, 2025 at 10:29:27 AM
CAS classification : [_separable]

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

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

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

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

✓ Mathematica. Time used: 0.129 (sec). Leaf size: 31

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

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

✓ Sympy. Time used: 0.504 (sec). Leaf size: 36

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

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