Internal problem ID [12887]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 4. Forcing and Resonance. Section 4.2 page 412
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+13 y=3 \cos \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(t),t$2)+4*diff(y(t),t)+13*y(t)=3*cos(2*t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{-2 t} \sin \left (3 t \right )+c_{1} {\mathrm e}^{-2 t} \cos \left (3 t \right )+\frac {24 \sin \left (2 t \right )}{145}+\frac {27 \cos \left (2 t \right )}{145} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 47
DSolve[y''[t]+4*y'[t]+13*y[t]==3*Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {3}{145} (8 \sin (2 t)+9 \cos (2 t))+c_2 e^{-2 t} \cos (3 t)+c_1 e^{-2 t} \sin (3 t) \]