74.11.24 problem 36

Internal problem ID [16274]
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 : Tuesday, January 28, 2025 at 09:00:02 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve(diff(y(t),t$2)-5*diff(y(t),t)+6*y(t)=-78*cos(3*t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 31

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

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