Internal problem ID [14855]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 34.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y={\mathrm e}^{t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(t),t$3)+3*diff(y(t),t$2)-9*diff(y(t),t)+5*y(t)=exp(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (\left (12 c_{3} t +t^{2}+12 c_{1} \right ) {\mathrm e}^{6 t}+12 c_{2} \right ) {\mathrm e}^{-5 t}}{12} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 39
DSolve[y'''[t]+3*y''[t]-9*y'[t]+5*y[t]==Exp[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^t \left (\frac {t^2}{12}+\left (-\frac {1}{36}+c_3\right ) t+\frac {1}{216}+c_2\right )+c_1 e^{-5 t} \]