Internal problem ID [14901]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 5. Applications of Higher Order Equations. Exercises 5.1, page 232
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+9 x=0} \] With initial conditions \begin {align*} \left [x \left (0\right ) = {\frac {1}{3}}, x^{\prime }\left (0\right ) = -1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(x(t),t$2)+9*x(t)=0,x(0) = 1/3, D(x)(0) = -1],x(t), singsol=all)
\[ x \left (t \right ) = -\frac {\sin \left (3 t \right )}{3}+\frac {\cos \left (3 t \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 20
DSolve[{x''[t]+9*x[t]==0,{x[0]==1/3,x'[0]==-1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{3} (\cos (3 t)-\sin (3 t)) \]