84.38.1 problem 26.13

Internal problem ID [22355]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 26. Solutions of linear differential equations with constant coefficients by Laplace transform. Supplementary problems
Problem number : 26.13
Date solved : Thursday, October 02, 2025 at 08:37:53 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: 0.029 (sec). Leaf size: 8

ode:=diff(y(t),t)+2*y(t) = 0; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 10

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

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

✓ Sympy. Time used: 0.058 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*y(t) + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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