Internal problem ID [14685]
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: 10.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+38 y^{\prime \prime }-64 y^{\prime }+40 y=153 \,{\mathrm e}^{-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(t),t$4)-10*diff(y(t),t$3)+38*diff(y(t),t$2)-64*diff(y(t),t)+40*y(t)=153*exp(-t),y(t), singsol=all)
\[ y \left (t \right ) = \left (t c_{2} +c_{1} \right ) {\mathrm e}^{2 t}+\left (\cos \left (t \right ) c_{3} +\sin \left (t \right ) c_{4} \right ) {\mathrm e}^{3 t}+{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 48
DSolve[y''''[t]-10*y'''[t]+38*y''[t]-64*y'[t]+40*y[t]==153*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t}+c_3 e^{2 t}+c_4 e^{2 t} t+c_2 e^{3 t} \cos (t)+c_1 e^{3 t} \sin (t) \]