Internal problem ID [14697]
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: 22.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-13 y^{\prime }+12 y=\cos \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(t),t$3)-13*diff(y(t),t)+12*y(t)=cos(t),y(t), singsol=all)
\[ y \left (t \right ) = \left (\left (\frac {3 \cos \left (t \right )}{85}-\frac {7 \sin \left (t \right )}{170}\right ) {\mathrm e}^{4 t}+c_{3} {\mathrm e}^{7 t}+c_{1} {\mathrm e}^{5 t}+c_{2} \right ) {\mathrm e}^{-4 t} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 40
DSolve[y'''[t]-13*y'[t]+12*y[t]==Cos[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {7 \sin (t)}{170}+\frac {3 \cos (t)}{85}+c_1 e^{-4 t}+c_2 e^t+c_3 e^{3 t} \]