Internal problem ID [14682]
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: 7.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y=2 \,{\mathrm e}^{-3 t}-t \,{\mathrm e}^{-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(diff(y(t),t$3)+6*diff(y(t),t$2)+11*diff(y(t),t)+6*y(t)=2*exp(-3*t)-t*exp(-t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (-2 t^{2}+8 c_{3} +6 t -7\right ) {\mathrm e}^{-t}}{8}+\frac {\left (3+2 t +2 c_{1} \right ) {\mathrm e}^{-3 t}}{2}+c_{2} {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 50
DSolve[y'''[t]+6*y''[t]+11*y'[t]+6*y[t]==2*Exp[-3*t]-t*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} e^{-3 t} \left (e^{2 t} \left (-2 t^2+6 t-7+8 c_3\right )+8 t+8 c_2 e^t+12+8 c_1\right ) \]