66.16.7 problem 7

Internal problem ID [16190]
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 : 7
Date solved : Thursday, October 02, 2025 at 10:43:24 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{4 t} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

ode:=diff(diff(y(t),t),t)-5*diff(y(t),t)+4*y(t) = exp(4*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {{\mathrm e}^{t} \left (3 c_2 +\left (3 c_1 +t \right ) {\mathrm e}^{3 t}\right )}{3} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 29

ode=D[y[t],{t,2}]-5*D[y[t],t]+4*y[t]==Exp[4*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_1 e^t+e^{4 t} \left (\frac {t}{3}-\frac {1}{9}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) - exp(4*t) - 5*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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