Internal problem ID [11700]
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 (vii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+10 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+10*y(t)=0,y(0) = 3, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-t} \left (3 \cos \left (3 t \right )+\sin \left (3 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 22
DSolve[{y''[t]+2*y'[t]+10*y[t]==0,{y[0]==3,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t} (\sin (3 t)+3 \cos (3 t)) \]