Internal problem ID [11703]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number: 12.1 (x).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+6 x^{\prime }+10 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 3, x^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve([diff(x(t),t$2)+6*diff(x(t),t)+10*x(t)=0,x(0) = 3, D(x)(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{-3 t} \left (3 \cos \left (t \right )+10 \sin \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 20
DSolve[{x''[t]+6*x'[t]+10*x[t]==0,{x[0]==3,x'[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{-3 t} (10 \sin (t)+3 \cos (t)) \]