Internal problem ID [14667]
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: 48.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {2 y^{\left (5\right )}+7 y^{\prime \prime \prime \prime }+17 y^{\prime \prime \prime }+17 y^{\prime \prime }+5 y^{\prime }=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = -3, y^{\prime }\left (0\right ) = {\frac {15}{2}}, y^{\prime \prime }\left (0\right ) = {\frac {17}{4}}, y^{\prime \prime \prime }\left (0\right ) = -{\frac {385}{8}}, y^{\prime \prime \prime \prime }\left (0\right ) = {\frac {1217}{16}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 29
dsolve([2*diff(y(t),t$5)+7*diff(y(t),t$4)+17*diff(y(t),t$3)+17*diff(y(t),t$2)+5*diff(y(t),t)=0,y(0) = -3, D(y)(0) = 15/2, (D@@2)(y)(0) = 17/4, (D@@3)(y)(0) = -385/8, (D@@4)(y)(0) = 1217/16],y(t), singsol=all)
\[ y \left (t \right ) = \left (2 \sin \left (2 t \right )-4 \cos \left (2 t \right )\right ) {\mathrm e}^{-t}+{\mathrm e}^{-\frac {t}{2}} \]
✓ Solution by Mathematica
Time used: 0.298 (sec). Leaf size: 31
DSolve[{2*y'''''[t]+7*y''''[t]+17*y'''[t]+17*y''[t]+5*y'[t]==0,{y[0]==-3,y'[0]==15/2,y''[0]==17/4,y'''[0]==-385/8,y''''[0]==1217/16}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t} \left (e^{t/2}+2 \sin (2 t)-4 \cos (2 t)\right ) \]