Internal problem ID [14662]
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: 43.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 8, y^{\prime \prime \prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(y(t),t$4)-8*diff(y(t),t$2)+16*y(t)=0,y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 8, (D@@3)(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -t \left (-{\mathrm e}^{2 t}+{\mathrm e}^{-2 t}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 19
DSolve[{y''''[t]-8*y''[t]+16*y[t]==0,{y[0]==0,y'[0]==0,y''[0]==8,y'''[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-2 t} \left (e^{4 t}-1\right ) t \]