Internal problem ID [14590]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-12 y^{\prime }+37 y={\mathrm e}^{6 t} \sec \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (t \right ) = \left (-\cos \left (t \right ) \ln \left (\sec \left (t \right )\right )+\cos \left (t \right ) c_{1} +\sin \left (t \right ) \left (c_{2} +t \right )\right ) {\mathrm e}^{6 t} \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 28
DSolve[y''[t]-12*y'[t]+37*y[t]==Exp[6*t]*Sec[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{6 t} ((t+c_1) \sin (t)+\cos (t) (\log (\cos (t))+c_2)) \]