68.12.16 problem 16

Internal problem ID [17610]
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 : 16
Date solved : Thursday, October 02, 2025 at 02:26:14 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 t} \sec \left (t \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(diff(y(t),t),t)-8*diff(y(t),t)+17*y(t) = exp(4*t)*sec(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{4 t} \left (-\ln \left (\sec \left (t \right )\right ) \cos \left (t \right )+c_1 \cos \left (t \right )+\sin \left (t \right ) \left (t +c_2 \right )\right ) \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 28

ode=D[y[t],{t,2}]-8*D[y[t],t]+17*y[t]==Exp[4*t]*Sec[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{4 t} ((t+c_1) \sin (t)+\cos (t) (\log (\cos (t))+c_2)) \end{align*}

✓ Sympy. Time used: 0.249 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(17*y(t) - exp(4*t)/cos(t) - 8*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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