68.11.15 problem 27

Internal problem ID [17552]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 27
Date solved : Thursday, October 02, 2025 at 02:25:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=32 t \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(diff(y(t),t),t)-2*diff(y(t),t)-8*y(t) = 32*t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-2 t} c_2 +{\mathrm e}^{4 t} c_1 -4 t +1 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 26

ode=D[y[t],{t,2}]-2*D[y[t],t]-8*y[t]==32*t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -4 t+c_1 e^{-2 t}+c_2 e^{4 t}+1 \end{align*}

✓ Sympy. Time used: 0.105 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-32*t - 8*y(t) - 2*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 2 t} + C_{2} e^{4 t} - 4 t + 1 \]