Internal problem ID [13235]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 6. Laplace transform. Section 6.6. page 624
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+2 y=\sin \left (4 t \right ) {\mathrm e}^{-2 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 5.156 (sec). Leaf size: 37
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+2*y(t)=exp(-2*t)*sin(4*t),y(0) = 2, D(y)(0) = -2],y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{-2 t} \left (-7 \sin \left (4 t \right )+4 \cos \left (4 t \right )\right )}{130}+\frac {128 \left (\cos \left (t \right )+\frac {\sin \left (t \right )}{8}\right ) {\mathrm e}^{-t}}{65} \]
✓ Solution by Mathematica
Time used: 0.379 (sec). Leaf size: 41
DSolve[{y''[t]+2*y'[t]+2*y[t]==Exp[-2*t]*Sin[4*t],{y[0]==2,y'[0]==-2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{130} e^{-2 t} \left (32 e^t \sin (t)-7 \sin (4 t)+256 e^t \cos (t)+4 \cos (4 t)\right ) \]