Internal problem ID [14672]
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).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+6 y=0} \] 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: 0.031 (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)
\[ y \left (t \right ) = -\frac {{\mathrm e}^{-3 t}}{11}+\frac {4 \sqrt {2}\, \sin \left (\sqrt {2}\, t \right )}{11}+\frac {\cos \left (\sqrt {2}\, t \right )}{11} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 40
DSolve[{y'''[t]+3*y''[t]+2*y'[t]+6*y[t]==0,{y[0]==0,y'[0]==1,y''[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{11} \left (-e^{-3 t}+4 \sqrt {2} \sin \left (\sqrt {2} t\right )+\cos \left (\sqrt {2} t\right )\right ) \]