68.18.26 problem 32

Internal problem ID [17870]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 32
Date solved : Thursday, October 02, 2025 at 02:29:03 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y^{\prime }+20 y&=-2 \,{\mathrm e}^{t} t \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

ode:=diff(diff(y(t),t),t)+9*diff(y(t),t)+20*y(t) = -2*t*exp(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-5 t} c_2 +{\mathrm e}^{-4 t} c_1 +\frac {\left (-30 t +11\right ) {\mathrm e}^{t}}{450} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 34

ode=D[y[t],{t,2}]+9*D[y[t],t]+20*y[t]==-2*t*Exp[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{450} e^t (11-30 t)+c_1 e^{-5 t}+c_2 e^{-4 t} \end{align*}

✓ Sympy. Time used: 0.134 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t*exp(t) + 20*y(t) + 9*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 5 t} + C_{2} e^{- 4 t} - \frac {t e^{t}}{15} + \frac {11 e^{t}}{450} \]