Internal problem ID [14902]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {10 x^{\prime \prime }+\frac {x}{10}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = -5, x^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([10*diff(x(t),t$2)+1/10*x(t)=0,x(0) = -5, D(x)(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = 10 \sin \left (\frac {t}{10}\right )-5 \cos \left (\frac {t}{10}\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 22
DSolve[{10*x''[t]+1/10*x[t]==0,{x[0]==-5,x'[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -5 \left (\cos \left (\frac {t}{10}\right )-2 \sin \left (\frac {t}{10}\right )\right ) \]