72.21.5 problem 5

Internal problem ID [14975]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 6. Laplace transform. Section 6.6. page 624
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 07:26:06 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+16 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 9.404 (sec). Leaf size: 15

dsolve([diff(y(t),t$2)+16*y(t)=0,y(0) = 1, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = \cos \left (4 t \right )+\frac {\sin \left (4 t \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 18

DSolve[{D[y[t],{t,2}]+16*y[t]==0,{y[0]==1,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{4} \sin (4 t)+\cos (4 t) \]