43.3.3 problem 1(c)

Internal problem ID [8889]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number : 1(c)
Date solved : Tuesday, September 30, 2025 at 05:59:35 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

\[ y = 3+{\mathrm e}^{-{\mathrm e}^{x}} c_1 \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to 3+c_1 e^{-e^x}\\ y(x)&\to 3 \end{align*}

✓ Sympy. Time used: 0.142 (sec). Leaf size: 10

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

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