68.11.26 problem 38

Internal problem ID [17563]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 38
Date solved : Thursday, October 02, 2025 at 02:25:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

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

\[ y = {\mathrm e}^{5 t} c_2 +{\mathrm e}^{-4 t} c_1 +\frac {{\mathrm e}^{t}}{10} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 29

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

\begin{align*} y(t)&\to \frac {e^t}{10}+c_1 e^{-4 t}+c_2 e^{5 t} \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 20

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

\[ y{\left (t \right )} = C_{1} e^{- 4 t} + C_{2} e^{5 t} + \frac {e^{t}}{10} \]