Internal problem ID [13212]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+8 y=2 \cos \left (3 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve([diff(y(t),t$2)+6*diff(y(t),t)+8*y(t)=2*cos(3*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {4 \,{\mathrm e}^{-4 t}}{25}-\frac {2 \,{\mathrm e}^{-2 t}}{13}-\frac {2 \cos \left (3 t \right )}{325}+\frac {36 \sin \left (3 t \right )}{325} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 74
DSolve[{y''[t]+5*y'[t]+8*y[t]==2*Cos[3*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{791} e^{-5 t/2} \left (105 e^{5 t/2} \sin (3 t)-85 \sqrt {7} \sin \left (\frac {\sqrt {7} t}{2}\right )-7 e^{5 t/2} \cos (3 t)+7 \cos \left (\frac {\sqrt {7} t}{2}\right )\right ) \]