Internal problem ID [12894]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=2 \cos \left (2 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+y(t)=2*cos(2*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 \left (3-5 t \right ) {\mathrm e}^{-t}}{25}-\frac {6 \cos \left (2 t \right )}{25}+\frac {8 \sin \left (2 t \right )}{25} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 37
DSolve[{y''[t]+2*y'[t]+y[t]==2*Cos[2*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {2}{25} e^{-t} \left (5 t-4 e^t \sin (2 t)+3 e^t \cos (2 t)-3\right ) \]