72.16.8 problem 8

Internal problem ID [14825]
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 : 8
Date solved : Thursday, March 13, 2025 at 04:20:27 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=4 \,{\mathrm e}^{-3 t} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 24

ode:=diff(diff(y(t),t),t)+diff(y(t),t)-6*y(t) = 4*exp(-3*t); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 32

ode=D[y[t],{t,2}]+D[y[t],t]-6*y[t]==4*Exp[-3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{25} e^{-3 t} \left (-20 t+25 c_2 e^{5 t}-4+25 c_1\right ) \]

✓ Sympy. Time used: 0.208 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-6*y(t) + Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 4*exp(-3*t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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