72.6.1 problem 1

Internal problem ID [14647]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.8 page 121
Problem number : 1
Date solved : Thursday, March 13, 2025 at 04:12:32 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=-4 y+9 \,{\mathrm e}^{-t} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(y(t),t) = -4*y(t)+9*exp(-t); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 21

ode=D[y[t],t]==-4*y[t]+9*Exp[-t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-4 t} \left (3 e^{3 t}+c_1\right ) \]

✓ Sympy. Time used: 0.156 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) + Derivative(y(t), t) - 9*exp(-t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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