69.33.1 problem 830

Internal problem ID [18570]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 3. Section 24.2. Solving the Cauchy problem for linear differential equation with constant coefficients. Exercises page 249
Problem number : 830
Date solved : Thursday, October 02, 2025 at 03:15:01 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} x^{\prime }+3 x&={\mathrm e}^{-2 t} \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.092 (sec). Leaf size: 15

ode:=diff(x(t),t)+3*x(t) = exp(-2*t); 
ic:=[x(0) = 0]; 
dsolve([ode,op(ic)],x(t),method='laplace');
 

\[ x = {\mathrm e}^{-2 t}-{\mathrm e}^{-3 t} \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 16

ode=D[x[t],t]+3*x[t]==Exp[-2*t]; 
ic={x[0]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^{-3 t} \left (e^t-1\right ) \end{align*}

✓ Sympy. Time used: 0.090 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(3*x(t) + Derivative(x(t), t) - exp(-2*t),0) 
ics = {x(0): 0} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \left (1 - e^{- t}\right ) e^{- 2 t} \]