49.2.4 problem 1(d)

Internal problem ID [7594]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1.6 Introduction– Linear equations of First Order. Page 41
Problem number : 1(d)
Date solved : Wednesday, March 05, 2025 at 04:47:23 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} 3 y^{\prime }+y&=2 \,{\mathrm e}^{-x} \end{align*}

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

ode:=3*diff(y(x),x)+y(x) = 2*exp(-x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -{\mathrm e}^{-x}+{\mathrm e}^{-\frac {x}{3}} c_{1} \]

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 23

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

\[ y(x)\to e^{-x} \left (-1+c_1 e^{2 x/3}\right ) \]

✓ Sympy. Time used: 0.218 (sec). Leaf size: 14

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

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