68.5.28 problem 28

Internal problem ID [17279]
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 : 28
Date solved : Thursday, October 02, 2025 at 02:00:43 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+3 t^{2} y&={\mathrm e}^{-t^{3}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 14

ode:=diff(y(t),t)+3*t^2*y(t) = exp(-t^3); 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \left (t +2\right ) {\mathrm e}^{-t^{3}} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 16

ode=D[y[t],t]+3*t^2*y[t]==Exp[-t^3]; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.153 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*t**2*y(t) + Derivative(y(t), t) - exp(-t**3),0) 
ics = {y(0): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (t + 2\right ) e^{- t^{3}} \]