86.2.9 problem 9

Internal problem ID [23083]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 3. Some standard types of differential equations. Exercise 3c at page 50
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:19:39 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} {\mathrm e}^{x} \left (y^{\prime }+y\right )&=3 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

\[ y = \left (3 x +c_1 \right ) {\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.102 (sec). Leaf size: 10

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

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