90.15.7 problem 7

Internal problem ID [25254]
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 251
Problem number : 7
Date solved : Thursday, October 02, 2025 at 11:59:22 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=25 \,{\mathrm e}^{2 t} t \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 31

ode:=diff(diff(y(t),t),t)+6*diff(y(t),t)+9*y(t) = 25*exp(2*t)*t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\left (5 t \,{\mathrm e}^{5 t}-2 \,{\mathrm e}^{5 t}+5 t c_1 +5 c_2 \right ) {\mathrm e}^{-3 t}}{5} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 29

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

\begin{align*} y(t)&\to e^{-3 t} \left (e^{5 t} \left (t-\frac {2}{5}\right )+c_2 t+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 48

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-25*t*exp(2*t) + 9*y(t) + 7*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} \sin {\left (\frac {3 \sqrt {7} t}{7} \right )} + C_{2} \cos {\left (\frac {3 \sqrt {7} t}{7} \right )} + \frac {25 t e^{2 t}}{37} - \frac {700 e^{2 t}}{1369} \]