90.14.8 problem 17

Internal problem ID [25236]
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 243
Problem number : 17
Date solved : Thursday, October 02, 2025 at 11:59:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(y(t),t),t)-y(t) = t^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{t} c_2 +{\mathrm e}^{-t} c_1 -t^{2}-2 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 26

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

\begin{align*} y(t)&\to -t^2+c_1 e^t+c_2 e^{-t}-2 \end{align*}

✓ Sympy. Time used: 0.048 (sec). Leaf size: 17

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

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