Internal problem ID [14898]
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: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+4 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(x(t),t$2)+4*x(t)=0,x(0) = 1, D(x)(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\sin \left (2 t \right )}{2}+\cos \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 15
DSolve[{x''[t]+4*x[t]==0,{x[0]==1,x'[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \cos (2 t)+\sin (t) \cos (t) \]