85.21.8 problem 1 (h)

Internal problem ID [22571]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 55
Problem number : 1 (h)
Date solved : Thursday, October 02, 2025 at 08:51:51 PM
CAS classification : [_linear]

\begin{align*} r^{\prime }&=t -\frac {r}{3 t} \end{align*}

With initial conditions

\begin{align*} r \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 15

ode:=diff(r(t),t) = t-1/3*r(t)/t; 
ic:=[r(1) = 1]; 
dsolve([ode,op(ic)],r(t), singsol=all);
 

\[ r = \frac {3 t^{2}}{7}+\frac {4}{7 t^{{1}/{3}}} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 22

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

\begin{align*} r(t)&\to \frac {3 t^2}{7}+\frac {4}{7 \sqrt [3]{t}} \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 17

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

\[ r{\left (t \right )} = \frac {3 t^{2}}{7} + \frac {4}{7 \sqrt [3]{t}} \]