72.16.1 problem 1

Internal problem ID [14818]
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 : 1
Date solved : Thursday, March 13, 2025 at 04:19:55 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 25

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

\[ y = \frac {\left ({\mathrm e}^{6 t}+6 c_{2} {\mathrm e}^{5 t}+6 c_{1} \right ) {\mathrm e}^{-2 t}}{6} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 31

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

\[ y(t)\to \frac {e^{4 t}}{6}+c_1 e^{-2 t}+c_2 e^{3 t} \]

✓ Sympy. Time used: 0.175 (sec). Leaf size: 22

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

\[ y{\left (t \right )} = C_{1} e^{- 2 t} + C_{2} e^{3 t} + \frac {e^{4 t}}{6} \]