Internal problem ID [4937]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-3 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (4) = -3, y^{\prime }\relax (4) = -17] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)-2*diff(y(t),t)-3*y(t)=0,y(4) = -3, D(y)(4) = -17],y(t), singsol=all)
\[ y \relax (t ) = 2 \,{\mathrm e}^{4-t}-5 \,{\mathrm e}^{-12+3 t} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 24
DSolve[{y''[t]-2*y'[t]-3*y[t]==0,{y[4]==-3,y'[4]==-17}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 e^{4-t}-5 e^{3 (t-4)} \\ \end{align*}