74.12.16 problem 16

Internal problem ID [16323]
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 : Tuesday, January 28, 2025 at 09:04:36 AM
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*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

dsolve(diff(y(t),t$2)-8*diff(y(t),t)+17*y(t)=exp(4*t)*sec(t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 28

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

\[ y(t)\to e^{4 t} ((t+c_1) \sin (t)+\cos (t) (\log (\cos (t))+c_2)) \]