72.16.3 problem 3

Internal problem ID [14820]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 4. Forcing and Resonance. Section 4.1 page 399
Problem number : 3
Date solved : Thursday, March 13, 2025 at 04:19:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=5 \,{\mathrm e}^{3 t} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 23

ode:=diff(diff(y(t),t),t)-diff(y(t),t)-2*y(t) = 5*exp(3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_{2} {\mathrm e}^{-t}+c_{1} {\mathrm e}^{2 t}+\frac {5 \,{\mathrm e}^{3 t}}{4} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 31

ode=D[y[t],{t,2}]-D[y[t],t]-2*y[t]==5*Exp[3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {5 e^{3 t}}{4}+c_1 e^{-t}+c_2 e^{2 t} \]

✓ Sympy. Time used: 0.177 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*y(t) - 5*exp(3*t) - Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- t} + C_{2} e^{2 t} + \frac {5 e^{3 t}}{4} \]