Internal problem ID [12893]
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: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+20 y=-3 \sin \left (2 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 44
dsolve([diff(y(t),t$2)+6*diff(y(t),t)+20*y(t)=-3*sin(2*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {3 \,{\mathrm e}^{-3 t} \sqrt {11}\, \sin \left (\sqrt {11}\, t \right )}{1100}-\frac {9 \,{\mathrm e}^{-3 t} \cos \left (\sqrt {11}\, t \right )}{100}-\frac {3 \sin \left (2 t \right )}{25}+\frac {9 \cos \left (2 t \right )}{100} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 61
DSolve[{y''[t]+6*y'[t]+20*y[t]==-3*Sin[2*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {3 e^{-3 t} \left (44 e^{3 t} \sin (2 t)+\sqrt {11} \sin \left (\sqrt {11} t\right )-33 e^{3 t} \cos (2 t)+33 \cos \left (\sqrt {11} t\right )\right )}{1100} \]