Internal problem ID [4930]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {y}{4}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 12, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)-1/4*y(t)=0,y(0) = 12, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = 6 \,{\mathrm e}^{\frac {t}{2}}+6 \,{\mathrm e}^{-\frac {t}{2}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 13
DSolve[{y''[t]-1/4*y[t]==0,{y[0]==12,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 12 \cosh \left (\frac {t}{2}\right ) \\ \end{align*}