90.14.13 problem 22

Internal problem ID [25241]
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 : 22
Date solved : Thursday, October 02, 2025 at 11:59:15 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=25 t \,{\mathrm e}^{-3 t} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=diff(diff(y(t),t),t)+6*diff(y(t),t)+9*y(t) = 25*t*exp(-3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-3 t} \left (c_2 +t c_1 +\frac {25}{6} t^{3}\right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 29

ode=D[y[t],{t,2}]+6*D[y[t],{t,1}]+9*y[t]==25*t*Exp[-3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{6} e^{-3 t} \left (25 t^3+6 c_2 t+6 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.175 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-25*t*exp(-3*t) + 9*y(t) + 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} + t \left (C_{2} + \frac {25 t^{2}}{6}\right )\right ) e^{- 3 t} \]