Internal problem ID [14666]
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: 47.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {8 y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+66 y^{\prime \prime \prime }-41 y^{\prime \prime }-37 y^{\prime }=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = -14, y^{\prime \prime }\left (0\right ) = -14, y^{\prime \prime \prime }\left (0\right ) = 139, y^{\prime \prime \prime \prime }\left (0\right ) = -{\frac {29}{4}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 23
dsolve([8*diff(y(t),t$5)+4*diff(y(t),t$4)+66*diff(y(t),t$3)-41*diff(y(t),t$2)-37*diff(y(t),t)=0,y(0) = 4, D(y)(0) = -14, (D@@2)(y)(0) = -14, (D@@3)(y)(0) = 139, (D@@4)(y)(0) = -29/4],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-\frac {t}{2}} \left (1-4 \sin \left (3 t \right )+3 \cos \left (3 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.326 (sec). Leaf size: 27
DSolve[{8*y'''''[t]+4*y''''[t]+66*y'''[t]-41*y''[t]-37*y'[t]==0,{y[0]==4,y'[0]==-14,y''[0]==-14,y'''[0]==139,y''''[0]==-29/4}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t/2} (-4 \sin (3 t)+3 \cos (3 t)+1) \]