39.1.5 problem Problem 11.5

Internal problem ID [6510]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page 95
Problem number : Problem 11.5
Date solved : Wednesday, March 05, 2025 at 12:54:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=64 \,{\mathrm e}^{-t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 31

ode:=diff(diff(y(t),t),t)-6*diff(y(t),t)+25*y(t) = 64*exp(-t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{3 t} \sin \left (4 t \right ) c_2 +{\mathrm e}^{3 t} \cos \left (4 t \right ) c_1 +2 \,{\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 37

ode=D[y[t],{t,2}]-6*D[y[t],t]+25*y[t]==64*Exp[-t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-t} \left (c_2 e^{4 t} \cos (4 t)+c_1 e^{4 t} \sin (4 t)+2\right ) \]

✓ Sympy. Time used: 0.225 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(25*y(t) - 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 64*exp(-t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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