74.13.36 problem 63 (a)

Internal problem ID [16402]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 63 (a)
Date solved : Tuesday, January 28, 2025 at 09:07:31 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 30

dsolve([diff(y(t),t$3)+3*diff(y(t),t$2)+2*diff(y(t),t)+6*y(t)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = -1],y(t), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{-3 t}}{11}+\frac {4 \sqrt {2}\, \sin \left (\sqrt {2}\, t \right )}{11}+\frac {\cos \left (\sqrt {2}\, t \right )}{11} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 40

DSolve[{D[ y[t],{t,3}]+3*D[y[t],{t,2}]+2*D[y[t],t]+6*y[t]==0,{y[0]==0,Derivative[1][y][0] ==1,Derivative[2][y][0] ==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{11} \left (-e^{-3 t}+4 \sqrt {2} \sin \left (\sqrt {2} t\right )+\cos \left (\sqrt {2} t\right )\right ) \]