Internal problem ID [12890]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=\cos \left (3 t \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(diff(y(t),t$2)+2*diff(y(t),t)+y(t)=cos(3*t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{-t}+{\mathrm e}^{-t} t c_{1} -\frac {2 \cos \left (3 t \right )}{25}+\frac {3 \sin \left (3 t \right )}{50} \]
✓ Solution by Mathematica
Time used: 0.22 (sec). Leaf size: 35
DSolve[y''[t]+2*y'[t]+y[t]==Cos[3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {3}{50} \sin (3 t)-\frac {2}{25} \cos (3 t)+e^{-t} (c_2 t+c_1) \]