76.15.1 problem 1

Internal problem ID [17563]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.5 (Nonhomogeneous Equations, Method of Undetermined Coefficients). Problems at page 260
Problem number : 1
Date solved : Thursday, March 13, 2025 at 10:13:02 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 23

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

\[ y = c_{2} {\mathrm e}^{3 t}+{\mathrm e}^{-t} c_{1} -{\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 22

ode=D[y[t],{t,2}]-2*D[y[t],t]-3*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-t} \left (c_2 e^{4 t}+c_1\right ) \]

✓ Sympy. Time used: 0.177 (sec). Leaf size: 19

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

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