68.6.5 problem 5

Internal problem ID [17315]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 5
Date solved : Thursday, October 02, 2025 at 02:02:17 PM
CAS classification : [_separable]

\begin{align*} 3 t y^{2}+y^{3} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 31

ode:=3*t*y(t)^2+y(t)^3*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= 0 \\ y &= \sqrt {-3 t^{2}+c_1} \\ y &= -\sqrt {-3 t^{2}+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 49

ode=3*t*y[t]^2+y[t]^3*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.335 (sec). Leaf size: 29

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

\[ \left [ y{\left (t \right )} = 0, \ y{\left (t \right )} = - \sqrt {C_{1} - 3 t^{2}}, \ y{\left (t \right )} = \sqrt {C_{1} - 3 t^{2}}\right ] \]