68.6.13 problem 14

Internal problem ID [17323]
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 : 14
Date solved : Thursday, October 02, 2025 at 02:02:32 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 11

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

\begin{align*} y(t)&\to c_1 t^3 \end{align*}

✓ Sympy. Time used: 0.068 (sec). Leaf size: 7

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

\[ y{\left (t \right )} = C_{1} t^{3} \]