Internal problem ID [14661]
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: 42.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+16 y^{\prime \prime \prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1, y^{\prime \prime }\left (0\right ) = 0, y^{\prime \prime \prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve([diff(y(t),t$4)+16*diff(y(t),t$3)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {1}{4096}+\frac {255 t}{256}+\frac {t^{2}}{32}-\frac {{\mathrm e}^{-16 t}}{4096} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 26
DSolve[{y''''[t]+16*y'''[t]==0,{y[0]==0,y'[0]==1,y''[0]==0,y'''[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {128 t^2+4080 t-e^{-16 t}+1}{4096} \]