Internal problem ID [13552]
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: 28.9 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-9 y=24 \,{\mathrm e}^{-3 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 6, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 22
dsolve([diff(y(t),t$2)-9*y(t)=24*exp(-3*t),y(0) = 6, D(y)(0) = 2],y(t), singsol=all)
\[ y \left (t \right ) = \left (-4 t +2\right ) {\mathrm e}^{-3 t}+4 \,{\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 23
DSolve[{y''[t]-9*y[t]==24*Exp[-3*t],{y[0]==6,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-3 t} \left (-4 t+4 e^{6 t}+2\right ) \]