Internal problem ID [14665]
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: 46.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-16 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 2, y^{\prime \prime }\left (0\right ) = 4, y^{\prime \prime \prime }\left (0\right ) = -24] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve([diff(y(t),t$4)-16*y(t)=0,y(0) = 1, D(y)(0) = 2, (D@@2)(y)(0) = 4, (D@@3)(y)(0) = -24],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-2 t}+2 \sin \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 17
DSolve[{y''''[t]-16*y[t]==0,{y[0]==1,y'[0]==2,y''[0]==4,y'''[0]==-24}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-2 t}+2 \sin (2 t) \]