Internal problem ID [4928]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 6. Laplace Transforms. Problem set 6.2, page 216
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }-6 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 11, y^{\prime }\relax (0) = 28] \end {align*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 15
dsolve([diff(y(t),t$2)-diff(y(t),t)-6*y(t)=0,y(0) = 11, D(y)(0) = 28],y(t), singsol=all)
\[ y \relax (t ) = 10 \,{\mathrm e}^{-2 t} {\mathrm e}^{5 t}+{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[{y''[t]-y'[t]-6*y[t]==0,{y[0]==11,y'[0]==28}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-2 t}+10 e^{3 t} \\ \end{align*}