Internal problem ID [12891]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+8 y=\cos \left (t \right )} \] 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: 25
dsolve([diff(y(t),t$2)+6*diff(y(t),t)+8*y(t)=cos(t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 \,{\mathrm e}^{-4 t}}{17}+\frac {7 \cos \left (t \right )}{85}+\frac {6 \sin \left (t \right )}{85}-\frac {{\mathrm e}^{-2 t}}{5} \]
✓ Solution by Mathematica
Time used: 2.147 (sec). Leaf size: 63
DSolve[{y''[t]+5*y'[t]+8*y[t]==Cos[t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{518} \left (35 \sin (t)-45 \sqrt {7} e^{-5 t/2} \sin \left (\frac {\sqrt {7} t}{2}\right )+49 \cos (t)-49 e^{-5 t/2} \cos \left (\frac {\sqrt {7} t}{2}\right )\right ) \]