74.14.22 problem 22

Internal problem ID [16427]
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
Date solved : Tuesday, January 28, 2025 at 09:07:50 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-13 y^{\prime }+12 y&=\cos \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 37

dsolve(diff(y(t),t$3)-13*diff(y(t),t)+12*y(t)=cos(t),y(t), singsol=all)
 

\[ y = \left (\left (\frac {3 \cos \left (t \right )}{85}-\frac {7 \sin \left (t \right )}{170}\right ) {\mathrm e}^{4 t}+c_{3} {\mathrm e}^{7 t}+c_{1} {\mathrm e}^{5 t}+c_{2} \right ) {\mathrm e}^{-4 t} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 102

DSolve[D[ y[t],{t,3}]-13*D[y[t],t]+12*y[t]==Cos[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} \left (\int _1^t\frac {1}{35} e^{4 K[1]} \cos (K[1])dK[1]+e^{5 t} \int _1^t-\frac {1}{10} e^{-K[2]} \cos (K[2])dK[2]+e^{7 t} \int _1^t\frac {1}{14} e^{-3 K[3]} \cos (K[3])dK[3]+c_2 e^{5 t}+c_3 e^{7 t}+c_1\right ) \]