33.5.1 problem Problem 24.17

Internal problem ID [7830]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page 248
Problem number : Problem 24.17
Date solved : Tuesday, September 30, 2025 at 05:06:06 PM
CAS classification : [_quadrature]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.086 (sec). Leaf size: 8

ode:=diff(y(x),x)+2*y(x) = 0; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 10

ode=D[y[x],x]+2*y[x]==0; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.059 (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): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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