74.14.23 problem 23

Internal problem ID [16428]
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 : 23
Date solved : Tuesday, January 28, 2025 at 09:07:51 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=\cos \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 28

dsolve(diff(y(t),t$3)+3*diff(y(t),t$2)+2*diff(y(t),t)=cos(t),y(t), singsol=all)
 

\[ y = \frac {c_{1} {\mathrm e}^{-2 t}}{2}-c_{2} {\mathrm e}^{-t}-\frac {3 \cos \left (t \right )}{10}+\frac {\sin \left (t \right )}{10}+c_{3} \]

✓ Solution by Mathematica

Time used: 20.521 (sec). Leaf size: 72

DSolve[D[ y[t],{t,3}]+3*D[y[t],{t,2}]+2*D[y[t],t]==Cos[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^te^{-2 K[3]} \left (c_1+e^{K[3]} c_2+\int _1^{K[3]}-e^{2 K[1]} \cos (K[1])dK[1]+e^{K[3]} \int _1^{K[3]}e^{K[2]} \cos (K[2])dK[2]\right )dK[3]+c_3 \]