Internal problem ID [13202]
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: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=5 \cos \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(t),t$2)+3*diff(y(t),t)+2*y(t)=5*cos(t),y(t), singsol=all)
\[ y \left (t \right ) = -{\mathrm e}^{-2 t} c_{1} +\frac {\cos \left (t \right )}{2}+\frac {3 \sin \left (t \right )}{2}+c_{2} {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 32
DSolve[y''[t]+3*y'[t]+2*y[t]==5*Cos[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} \left (3 \sin (t)+\cos (t)+2 e^{-2 t} \left (c_2 e^t+c_1\right )\right ) \]