75.33.1 problem 830

Internal problem ID [17283]
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 : Tuesday, January 28, 2025 at 09:58:52 AM
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*}

✓ Solution by Maple

Time used: 9.339 (sec). Leaf size: 15

dsolve([diff(x(t),t)+3*x(t)=exp(-2*t),x(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = {\mathrm e}^{-2 t}-{\mathrm e}^{-3 t} \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 16

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

\[ x(t)\to e^{-3 t} \left (e^t-1\right ) \]