90.12.8 problem 8

Internal problem ID [25210]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 213
Problem number : 8
Date solved : Thursday, October 02, 2025 at 11:58:59 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 26

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

\[ y = \sin \left (2 \sqrt {2}\, t \right ) c_2 +\cos \left (2 \sqrt {2}\, t \right ) c_1 +\frac {t}{8} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 35

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

\begin{align*} y(t)&\to \frac {t}{8}+c_1 \cos \left (2 \sqrt {2} t\right )+c_2 \sin \left (2 \sqrt {2} t\right ) \end{align*}

✓ Sympy. Time used: 0.033 (sec). Leaf size: 29

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

\[ y{\left (t \right )} = C_{1} \sin {\left (2 \sqrt {2} t \right )} + C_{2} \cos {\left (2 \sqrt {2} t \right )} + \frac {t}{8} \]