Internal problem ID [14681]
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: 6.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }+10 y^{\prime \prime }+34 y^{\prime }+40 y=t \,{\mathrm e}^{-4 t}+2 \,{\mathrm e}^{-3 t} \cos \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve(diff(y(t),t$3)+10*diff(y(t),t$2)+34*diff(y(t),t)+40*y(t)=t*exp(-4*t)+2*exp(-3*t)*cos(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (\left (-2 t +4 c_{2} +4\right ) \cos \left (t \right )+2 \sin \left (t \right ) \left (t +2 c_{3} +1\right )\right ) {\mathrm e}^{-3 t}}{4}+\frac {{\mathrm e}^{-4 t} \left (t^{2}+4 c_{1} +2 t +1\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.209 (sec). Leaf size: 57
DSolve[y'''[t]+10*y''[t]+34*y'[t]+40*y[t]==t*Exp[-4*t]+2*Exp[-3*t]*Cos[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} e^{-4 t} \left (t^2+2 t-e^t (2 t-3-4 c_2) \cos (t)+e^t (2 t+1+4 c_1) \sin (t)+1+4 c_3\right ) \]