74.12.46 problem 46

Internal problem ID [16353]
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 : 46
Date solved : Tuesday, January 28, 2025 at 09:06:37 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=65 \cos \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

dsolve(diff(y(t),t$2)+4*diff(y(t),t)+3*y(t)=65*cos(2*t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{-3 t} c_{2} +{\mathrm e}^{-t} c_{1} -\cos \left (2 t \right )+8 \sin \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 35

DSolve[D[y[t],{t,2}]+4*D[y[t],t]+3*y[t]==65*Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 8 \sin (2 t)-\cos (2 t)+e^{-3 t} \left (c_2 e^{2 t}+c_1\right ) \]