Internal problem ID [14621]
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: 46.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+3 y=65 \cos \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(t),t$2)+4*diff(y(t),t)+3*y(t)=65*cos(2*t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{-3 t}+{\mathrm e}^{-t} c_{1} -\cos \left (2 t \right )+8 \sin \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 35
DSolve[y''[t]+4*y'[t]+3*y[t]==65*Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 8 \sin (2 t)-\cos (2 t)+e^{-3 t} \left (c_2 e^{2 t}+c_1\right ) \]