68.3.20 problem 15

Internal problem ID [17167]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 15
Date solved : Thursday, October 02, 2025 at 01:48:59 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 14

ode:=t*diff(y(t),t)+y(t) = t^3; 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {t^{4}-1}{4 t} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 17

ode=t*D[y[t],t]+y[t]==t^3; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {t^4-1}{4 t} \end{align*}

✓ Sympy. Time used: 0.117 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = \frac {\frac {t^{4}}{4} - \frac {1}{4}}{t} \]