Internal problem ID [14651]
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: 32.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }+8 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(diff(y(t),t$4)+2*diff(y(t),t$3)-2*diff(y(t),t$2)+8*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \left (c_{3} {\mathrm e}^{3 t} \sin \left (t \right )+c_{4} {\mathrm e}^{3 t} \cos \left (t \right )+t c_{2} +c_{1} \right ) {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 38
DSolve[y''''[t]+2*y'''[t]-2*y''[t]+8*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-2 t} \left (c_4 t+c_2 e^{3 t} \cos (t)+c_1 e^{3 t} \sin (t)+c_3\right ) \]