Internal problem ID [14668]
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: 49.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}+8 y^{\prime \prime \prime \prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 8, y^{\prime }\left (0\right ) = 4, y^{\prime \prime }\left (0\right ) = 0, y^{\prime \prime \prime }\left (0\right ) = 48, y^{\prime \prime \prime \prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 14
dsolve([diff(y(t),t$5)+8*diff(y(t),t$4)=0,y(0) = 8, D(y)(0) = 4, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 48, (D@@4)(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 8 t^{3}+4 t +8 \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 15
DSolve[{y'''''[t]+8*y''''[t]==0,{y[0]==8,y'[0]==4,y''[0]==0,y'''[0]==48,y''''[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 4 \left (2 t^3+t+2\right ) \]