81.6.1 problem 7-1

Internal problem ID [21547]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 7. Linear Differential Equations. Page 101.
Problem number : 7-1
Date solved : Thursday, October 02, 2025 at 07:47:43 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 10

ode:=diff(y(x),x)+2*y(x) = 0; 
ic:=[y(0) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 4 \,{\mathrm e}^{-2 x} \]

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

ode=D[y[x],x]+2*y[x]==0; 
ic={y[0]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 4 e^{-2 x} \end{align*}

✓ Sympy. Time used: 0.065 (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): 4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 4 e^{- 2 x} \]