Internal problem ID [15567]
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: 844.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+4 x^{\prime }+4 x=4} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 13
dsolve([diff(x(t),t$2)+4*diff(x(t),t)+4*x(t)=4,x(0) = 1, D(x)(0) = -4],x(t), singsol=all)
\[ x = 1-4 t \,{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 15
DSolve[{x''[t]+4*x'[t]+4*x[t]==4,{x[0]==1,x'[0]==-4}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to 1-4 e^{-2 t} t \]