Internal problem ID [14654]
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: 35.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(t),t$5)+3*diff(y(t),t$4)+3*diff(y(t),t$3)+diff(y(t),t$2)=0,y(t), singsol=all)
\[ y \left (t \right ) = \left (c_{5} t^{2}+t c_{4} +c_{3} \right ) {\mathrm e}^{-t}+t c_{2} +c_{1} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 38
DSolve[y'''''[t]+3*y''''[t]+3*y'''[t]+y''[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t} \left (c_3 \left (t^2+4 t+6\right )+c_2 (t+2)+c_1\right )+c_5 t+c_4 \]