74.11.19 problem 31

Internal problem ID [16198]
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 : 31
Date solved : Monday, March 31, 2025 at 02:46:34 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 8 y^{\prime \prime }+6 y^{\prime }+y&=5 t^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

ode:=8*diff(diff(y(t),t),t)+6*diff(y(t),t)+y(t) = 5*t^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = -4 \,{\mathrm e}^{-\frac {t}{2}} c_1 +{\mathrm e}^{-\frac {t}{4}} c_2 +5 t^{2}-60 t +280 \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 35

ode=8*D[y[t],{t,2}]+6*D[y[t],t]+y[t]==5*t^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 5 t^2-60 t+c_1 e^{-t/4}+c_2 e^{-t/2}+280 \]

✓ Sympy. Time used: 0.188 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-5*t**2 + y(t) + 6*Derivative(y(t), t) + 8*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- \frac {t}{2}} + C_{2} e^{- \frac {t}{4}} + 5 t^{2} - 60 t + 280 \]