74.5.24 problem 24

Internal problem ID [15917]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 24
Date solved : Monday, March 31, 2025 at 02:13:11 PM
CAS classification : [_linear]

\begin{align*} p^{\prime }&=t^{3}+\frac {p}{t} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ p = \frac {\left (t^{3}+3 c_1 \right ) t}{3} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 17

ode=D[p[t],t]==t^3+p[t]/t; 
ic={}; 
DSolve[{ode,ic},p[t],t,IncludeSingularSolutions->True]
 

\[ p(t)\to \frac {t^4}{3}+c_1 t \]

✓ Sympy. Time used: 0.245 (sec). Leaf size: 10

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

\[ p{\left (t \right )} = t \left (C_{1} + \frac {t^{3}}{3}\right ) \]