73.10.1 problem 15.2 (a)

Internal problem ID [15296]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.2 (a)
Date solved : Tuesday, January 28, 2025 at 07:51:41 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)+4*y(x)=0,y(0) = 2, D(y)(0) = 6],y(x), singsol=all)
 

\[ y = 3 \sin \left (2 x \right )+2 \cos \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]+4*y[x]==0,{y[0]==2,Derivative[1][y][0] ==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 \sin (2 x)+2 \cos (2 x) \]