Internal problem ID [14696]
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: 21.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y={\mathrm e}^{-3 t}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(diff(y(t),t$3)+3*diff(y(t),t$2)-10*diff(y(t),t)-24*y(t)=exp(-3*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (6 c_{3} {\mathrm e}^{7 t}+6 c_{2} {\mathrm e}^{2 t}+{\mathrm e}^{t}+6 c_{1} \right ) {\mathrm e}^{-4 t}}{6} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 40
DSolve[y'''[t]+3*y''[t]-10*y'[t]-24*y[t]==Exp[-3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{6} e^{-4 t} \left (e^t+6 c_2 e^{2 t}+6 c_3 e^{7 t}+6 c_1\right ) \]