Internal problem ID [15553]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {x^{\prime }+3 x={\mathrm e}^{-2 t}} \] With initial conditions \begin {align*} [x \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.454 (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: 0.096 (sec). Leaf size: 16
DSolve[{x'[t]+3*x[t]==Exp[-2*t],{x[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{-3 t} \left (e^t-1\right ) \]