Internal problem ID [12838]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Review Exercises for chapter 3. page 376
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=0,y(0) = 3, D(y)(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-t} \left (\sin \left (2 t \right )+3 \cos \left (2 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 22
DSolve[{y''[t]+2*y'[t]+5*y[t]==0,{y[0]==3,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t} (\sin (2 t)+3 \cos (2 t)) \]