68.5.6 problem 6

Internal problem ID [17257]
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 : 6
Date solved : Thursday, October 02, 2025 at 02:00:02 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 19

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

\begin{align*} y(t)&\to \frac {t^2}{3}+\frac {c_1}{t} \end{align*}

✓ Sympy. Time used: 0.106 (sec). Leaf size: 10

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

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