Internal problem ID [14649]
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: 30.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }-y^{\prime \prime }+54 y^{\prime }-72 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(diff(y(t),t$4)-6*diff(y(t),t$3)-diff(y(t),t$2)+54*diff(y(t),t)-72*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \left ({\mathrm e}^{7 t} c_{2} +c_{3} {\mathrm e}^{6 t}+c_{4} {\mathrm e}^{5 t}+c_{1} \right ) {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 36
DSolve[y''''[t]-6*y'''[t]-y''[t]+54*y'[t]-72*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-3 t} \left (e^{5 t} \left (e^t \left (c_4 e^t+c_3\right )+c_2\right )+c_1\right ) \]