Internal problem ID [13215]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+y=\cos \left (3 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(t),t$2)+3*diff(y(t),t)+y(t)=cos(3*t),y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{\frac {\left (\sqrt {5}-3\right ) t}{2}} c_{2} +{\mathrm e}^{-\frac {\left (3+\sqrt {5}\right ) t}{2}} c_{1} -\frac {8 \cos \left (3 t \right )}{145}+\frac {9 \sin \left (3 t \right )}{145} \]
✓ Solution by Mathematica
Time used: 0.674 (sec). Leaf size: 52
DSolve[y''[t]+3*y'[t]+y[t]==Cos[3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {9}{145} \sin (3 t)-\frac {8}{145} \cos (3 t)+e^{-\frac {1}{2} \left (3+\sqrt {5}\right ) t} \left (c_2 e^{\sqrt {5} t}+c_1\right ) \]