Internal problem ID [14499]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=0,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{-t} \left (2 \cos \left (2 t \right )+\sin \left (2 t \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 25
DSolve[{y''[t]+2*y'[t]+5*y[t]==0,{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-t} (\sin (2 t)+2 \cos (2 t)) \]