74.11.17 problem 29

Internal problem ID [16188]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 29
Date solved : Thursday, March 13, 2025 at 07:55:18 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+26 y&=-338 t \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

ode:=diff(diff(y(t),t),t)+2*diff(y(t),t)+26*y(t) = -338*t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-t} \sin \left (5 t \right ) c_{2} +\cos \left (5 t \right ) {\mathrm e}^{-t} c_{1} -13 t +1 \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 34

ode=D[y[t],{t,2}]+2*D[y[t],t]+26*y[t]==-338*t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -13 t+c_2 e^{-t} \cos (5 t)+c_1 e^{-t} \sin (5 t)+1 \]

✓ Sympy. Time used: 0.179 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(338*t + 26*y(t) + 2*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - 13 t + \left (C_{1} \sin {\left (5 t \right )} + C_{2} \cos {\left (5 t \right )}\right ) e^{- t} + 1 \]