65.6.7 problem 12.1 (vii)

Internal problem ID [13756]
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)
Date solved : Tuesday, January 28, 2025 at 06:02:01 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=0 \end{align*}

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)
 

\[ y = {\mathrm e}^{-t} \left (\sin \left (3 t \right )+3 \cos \left (3 t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 22

DSolve[{D[y[t],{t,2}]+2*D[y[t],t]+10*y[t]==0,{y[0]==3,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} (\sin (3 t)+3 \cos (3 t)) \]