68.12.2 problem 2

Internal problem ID [17596]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 2
Date solved : Thursday, October 02, 2025 at 02:26:03 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+16 y^{\prime }&=t \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=diff(diff(y(t),t),t)+16*diff(y(t),t) = t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {t^{2}}{32}-\frac {{\mathrm e}^{-16 t} c_1}{16}-\frac {t}{256}+c_2 \]

✓ Mathematica. Time used: 2.662 (sec). Leaf size: 42

ode=D[y[t],{t,2}]+16*D[y[t],t]==t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \int _1^te^{-16 K[2]} \left (c_1+\int _1^{K[2]}e^{16 K[1]} K[1]dK[1]\right )dK[2]+c_2 \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t + 16*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + C_{2} e^{- 16 t} + \frac {t^{2}}{32} - \frac {t}{256} \]