75.33.15 problem 844

Internal problem ID [17297]
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
Date solved : Tuesday, January 28, 2025 at 09:59:01 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&=4 \end{align*}

Using Laplace method With initial conditions

\begin{align*} x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 8.582 (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)
 

\[ x \left (t \right ) = 1-4 t \,{\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 15

DSolve[{D[x[t],{t,2}]+4*D[x[t],t]+4*x[t]==4,{x[0]==1,Derivative[1][x][0 ]==-4}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 1-4 e^{-2 t} t \]