74.12.15 problem 15

Internal problem ID [16322]
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 : 15
Date solved : Tuesday, January 28, 2025 at 09:04:31 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-12 y^{\prime }+37 y&={\mathrm e}^{6 t} \sec \left (t \right ) \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(t),t$2)-12*diff(y(t),t)+37*y(t)=exp(6*t)*sec(t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{6 t} \left (-\cos \left (t \right ) \ln \left (\sec \left (t \right )\right )+\cos \left (t \right ) c_{1} +\sin \left (t \right ) \left (c_{2} +t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 28

DSolve[D[y[t],{t,2}]-12*D[y[t],t]+37*y[t]==Exp[6*t]*Sec[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{6 t} ((t+c_1) \sin (t)+\cos (t) (\log (\cos (t))+c_2)) \]