46.6.5 problem 5

Internal problem ID [7351]
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
Date solved : Monday, January 27, 2025 at 02:50:52 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-\frac {y}{4}&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=12\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.228 (sec). Leaf size: 10

dsolve([diff(y(t),t$2)-1/4*y(t)=0,y(0) = 12, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = 12 \cosh \left (\frac {t}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 19

DSolve[{D[y[t],{t,2}]-1/4*y[t]==0,{y[0]==12,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 6 e^{-t/2} \left (e^t+1\right ) \]