68.11.24 problem 36

Internal problem ID [17561]
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 : 36
Date solved : Thursday, October 02, 2025 at 02:25:26 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=-78 \cos \left (3 t \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

ode:=diff(diff(y(t),t),t)-5*diff(y(t),t)+6*y(t) = -78*cos(3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{2 t} c_2 +{\mathrm e}^{3 t} c_1 +5 \sin \left (3 t \right )+\cos \left (3 t \right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 31

ode=D[y[t],{t,2}]-5*D[y[t],t]+6*y[t]==-78*Cos[3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 5 \sin (3 t)+\cos (3 t)+e^{2 t} \left (c_2 e^t+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.132 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(6*y(t) + 78*cos(3*t) - 5*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{2 t} + C_{2} e^{3 t} + 5 \sin {\left (3 t \right )} + \cos {\left (3 t \right )} \]