Internal problem ID [14684]
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: 9.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y=-111 \,{\mathrm e}^{t}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(diff(y(t),t$3)+6*diff(y(t),t$2)-14*diff(y(t),t)-104*y(t)=-111*exp(t),y(t), singsol=all)
\[ y \left (t \right ) = \left ({\mathrm e}^{9 t} c_{1} +{\mathrm e}^{6 t}+c_{3} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) {\mathrm e}^{-5 t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 35
DSolve[y'''[t]+6*y''[t]-14*y'[t]-104*y[t]==-111*Exp[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-5 t} \left (e^{6 t}+c_3 e^{9 t}+c_2 \cos (t)+c_1 \sin (t)\right ) \]