Internal problem ID [5626]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.007 (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)
\[ y \relax (x ) = \frac {2 \sin \left (3 x \right )}{3}+\cos \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[{y''[x]+9*y[x]==0,{y[0]==1,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2}{3} \sin (3 x)+\cos (3 x) \\ \end{align*}