78.2.10 problem 4

Internal problem ID [20962]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 2, Second order ODEs. Problems section 2.6
Problem number : 4
Date solved : Thursday, October 02, 2025 at 07:00:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime }-3 x^{\prime }+2 x&=6 \,{\mathrm e}^{3 t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(diff(x(t),t),t)-3*diff(x(t),t)+2*x(t) = 6*exp(3*t); 
dsolve(ode,x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 25

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

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

✓ Sympy. Time used: 0.112 (sec). Leaf size: 19

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

\[ x{\left (t \right )} = \left (C_{1} + C_{2} e^{t} + 3 e^{2 t}\right ) e^{t} \]