Internal problem ID [14585]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+25 y={\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (t \right ) = -\frac {\left (-\frac {\ln \left (\cos \left (4 t \right )\right ) \cos \left (4 t \right )}{4}-\frac {\ln \left (\sin \left (4 t \right )\right ) \sin \left (4 t \right )}{4}+\left (-4 c_{1} +t \right ) \cos \left (4 t \right )-\sin \left (4 t \right ) \left (t +4 c_{2} \right )\right ) {\mathrm e}^{-3 t}}{4} \]
✓ Solution by Mathematica
Time used: 0.135 (sec). Leaf size: 52
DSolve[y''[t]+6*y'[t]+25*y[t]==Exp[-3*t]*(Sec[4*t]+Csc[4*t]),y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{16} e^{-3 t} (\cos (4 t) (-4 t+\log (\cos (4 t))+16 c_2)+\sin (4 t) (\log (\sin (4 t))+4 (t+4 c_1))) \]