73.11.33 problem 17.6 (c)

Internal problem ID [15347]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 17. Second order Homogeneous equations with constant coefficients. Additional exercises page 334
Problem number : 17.6 (c)
Date solved : Tuesday, January 28, 2025 at 07:53:24 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=12 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)+16*y(x)=0,y(0) = 4, D(y)(0) = 12],y(x), singsol=all)
 

\[ y = 3 \sin \left (4 x \right )+4 \cos \left (4 x \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]+16*y[x]==0,{y[0]==4,Derivative[1][y][0] ==12}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 \sin (4 x)+4 \cos (4 x) \]