Internal problem ID [14678]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number: 3.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}-y^{\prime \prime \prime \prime }=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(t),t$5)-diff(y(t),t$4)=1,y(t), singsol=all)
\[ y \left (t \right ) = -\frac {t^{4}}{24}+\frac {c_{3} t^{2}}{2}+\frac {c_{2} t^{3}}{6}+{\mathrm e}^{t} c_{1} +t c_{4} +c_{5} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 37
DSolve[y'''''[t]-y''''[t]==1,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {t^4}{24}+c_5 t^3+c_4 t^2+c_3 t+c_1 e^t+c_2 \]