74.12.10 problem 10

Internal problem ID [16317]
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 : 10
Date solved : Tuesday, January 28, 2025 at 09:03:23 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&={\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 54

dsolve(diff(y(t),t$2)+6*diff(y(t),t)+25*y(t)=exp(-3*t)*(sec(4*t)+csc(4*t)),y(t), singsol=all)
 

\[ y = -\frac {\left (-\frac {\ln \left (\cos \left (4 t \right )\right ) \cos \left (4 t \right )}{4}-\frac {\ln \left (\sin \left (4 t \right )\right ) \sin \left (4 t \right )}{4}+\left (t -4 c_{1} \right ) \cos \left (4 t \right )-\left (t +4 c_{2} \right ) \sin \left (4 t \right )\right ) {\mathrm e}^{-3 t}}{4} \]

✓ Solution by Mathematica

Time used: 0.126 (sec). Leaf size: 52

DSolve[D[y[t],{t,2}]+6*D[y[t],t]+25*y[t]==Exp[-3*t]*(Sec[4*t]+Csc[4*t]),y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{16} e^{-3 t} (\cos (4 t) (-4 t+\log (\cos (4 t))+16 c_2)+\sin (4 t) (\log (\sin (4 t))+4 (t+4 c_1))) \]