68.14.23 problem 23

Internal problem ID [17715]
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 : Thursday, October 02, 2025 at 02:27:18 PM
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*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=diff(diff(diff(y(t),t),t),t)+3*diff(diff(y(t),t),t)+2*diff(y(t),t) = cos(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-2 t} c_1}{2}-{\mathrm e}^{-t} c_2 -\frac {3 \cos \left (t \right )}{10}+\frac {\sin \left (t \right )}{10}+c_3 \]

✓ Mathematica. Time used: 11.67 (sec). Leaf size: 72

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

\begin{align*} 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 \end{align*}

✓ Sympy. Time used: 0.144 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-cos(t) + 2*Derivative(y(t), t) + 3*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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