74.11.16 problem 28

Internal problem ID [16195]
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 : 28
Date solved : Monday, March 31, 2025 at 02:46:30 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }-15 y&=75 t \end{align*}

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

ode:=16*diff(diff(y(t),t),t)-8*diff(y(t),t)-15*y(t) = 75*t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{\frac {5 t}{4}} c_2 +{\mathrm e}^{-\frac {3 t}{4}} c_1 -5 t +\frac {8}{3} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 32

ode=16*D[y[t],{t,2}]-8*D[y[t],t]-15*y[t]==75*t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -5 t+c_1 e^{-3 t/4}+c_2 e^{5 t/4}+\frac {8}{3} \]

✓ Sympy. Time used: 0.195 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-75*t - 15*y(t) - 8*Derivative(y(t), t) + 16*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- \frac {3 t}{4}} + C_{2} e^{\frac {5 t}{4}} - 5 t + \frac {8}{3} \]