68.1.40 problem 47

Internal problem ID [17107]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 47
Date solved : Thursday, October 02, 2025 at 01:43:16 PM
CAS classification : [_quadrature]

\begin{align*} 2 y+y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 10

ode:=diff(y(x),x)+2*y(x) = 0; 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 2 \,{\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 12

ode=D[y[x],x]+2*y[x]==0; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 e^{-2 x} \end{align*}

✓ Sympy. Time used: 0.060 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = 2 e^{- 2 x} \]