Internal problem ID [13863]
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: 28.6 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-9 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 9] \end {align*}
✓ Solution by Maple
Time used: 4.485 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)-9*y(t)=0,y(0) = 4, D(y)(0) = 9],y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{-3 t}}{2}+\frac {7 \,{\mathrm e}^{3 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 23
DSolve[{y''[t]-9*y[t]==0,{y[0]==4,y'[0]==9}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-3 t} \left (7 e^{6 t}+1\right ) \]