68.6.42 problem 48

Internal problem ID [17352]
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 : 48
Date solved : Thursday, October 02, 2025 at 02:10:11 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

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

\[ y = \frac {c_1}{t} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 16

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

\begin{align*} y(t)&\to \frac {c_1}{t}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.070 (sec). Leaf size: 5

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

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