Internal problem ID [12863]
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 4.1 page 399
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+6 y=-8} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve([diff(y(t),t$2)+4*diff(y(t),t)+6*y(t)=-8,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {4 \,{\mathrm e}^{-2 t} \sin \left (\sqrt {2}\, t \right ) \sqrt {2}}{3}+\frac {4 \,{\mathrm e}^{-2 t} \cos \left (\sqrt {2}\, t \right )}{3}-\frac {4}{3} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 44
DSolve[{y''[t]+4*y'[t]+6*y[t]==-8,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {4}{3} e^{-2 t} \left (-e^{2 t}+\sqrt {2} \sin \left (\sqrt {2} t\right )+\cos \left (\sqrt {2} t\right )\right ) \]