Internal problem ID [13868]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 28. The inverse Laplace transform. Additional Exercises. page 509
Problem number: 28.8 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+13 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 8] \end {align*}
✓ Solution by Maple
Time used: 4.75 (sec). Leaf size: 22
dsolve([diff(y(t),t$2)+6*diff(y(t),t)+13*y(t)=0,y(0) = 2, D(y)(0) = 8],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-3 t} \left (2 \cos \left (2 t \right )+7 \sin \left (2 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 24
DSolve[{y''[t]+6*y'[t]+13*y[t]==0,{y[0]==2,y'[0]==8}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-3 t} (7 \sin (2 t)+2 \cos (2 t)) \]