Internal problem ID [13549]
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 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+8 y^{\prime }+17 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -12] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 12
dsolve([diff(y(t),t$2)+8*diff(y(t),t)+17*y(t)=0,y(0) = 3, D(y)(0) = -12],y(t), singsol=all)
\[ y \left (t \right ) = 3 \,{\mathrm e}^{-4 t} \cos \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 14
DSolve[{y''[t]+8*y'[t]+17*y[t]==0,{y[0]==3,y'[0]==-12}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 3 e^{-4 t} \cos (t) \]