Internal problem ID [14894]
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: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {9 x^{\prime \prime }+4 x=0} \] With initial conditions \begin {align*} \left [x \left (0\right ) = -{\frac {1}{2}}, x^{\prime }\left (0\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([9*diff(x(t),t$2)+4*x(t)=0,x(0) = -1/2, D(x)(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = \frac {3 \sin \left (\frac {2 t}{3}\right )}{2}-\frac {\cos \left (\frac {2 t}{3}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 26
DSolve[{9*x''[t]+4*x[t]==0,{x[0]==-1/2,x'[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{2} \left (3 \sin \left (\frac {2 t}{3}\right )-\cos \left (\frac {2 t}{3}\right )\right ) \]