50.14.9 problem 2(a)

Internal problem ID [8047]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 2(a)
Date solved : Monday, January 27, 2025 at 03:37:58 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 15

dsolve([diff(y(x),x$2)+9*y(x)=0,y(0) = 1, D(y)(0) = 2],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]+9*y[x]==0,{y[0]==1,Derivative[1][y][0] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

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