72.7.2 problem 2

Internal problem ID [14672]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 2
Date solved : Monday, March 31, 2025 at 12:52:21 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {3 y}{t}+t^{5} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=diff(y(t),t) = 3*y(t)/t+t^5; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 19

ode=D[y[t],t]==3/t*y[t]+t^5; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {t^6}{3}+c_1 t^3 \]

✓ Sympy. Time used: 0.255 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**5 + Derivative(y(t), t) - 3*y(t)/t,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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