Internal problem ID [14669]
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: 50.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 16, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 0, y^{\prime \prime \prime }\left (0\right ) = 0, y^{\prime \prime \prime \prime }\left (0\right ) = 0, y^{\left (5\right )}\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 29
dsolve([diff(y(t),t$6)-3*diff(y(t),t$4)+3*diff(y(t),t$2)-y(t)=0,y(0) = 16, D(y)(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 0, (D@@4)(y)(0) = 0, (D@@5)(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \left (t^{2}+5 t +8\right ) {\mathrm e}^{-t}+{\mathrm e}^{t} \left (t^{2}-5 t +8\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 33
DSolve[{y''''''[t]-3*y''''[t]+3*y''[t]-y[t]==0,{y[0]==16,y'[0]==0,y''[0]==0,y'''[0]==0,y''''[0]==0,y'''''[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t} \left (t^2+e^{2 t} \left (t^2-5 t+8\right )+5 t+8\right ) \]