7.18.9 problem 9

Internal problem ID [538]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 4. Laplace transform methods. Section 4.2 (Transformation of initial value problems). Problems at page 287
Problem number : 9
Date solved : Monday, January 27, 2025 at 02:54:40 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&=1 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.188 (sec). Leaf size: 18

dsolve([diff(x(t),t$2)+4*diff(x(t),t)+3*x(t)=1,x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {{\mathrm e}^{-3 t}}{6}+\frac {1}{3}-\frac {{\mathrm e}^{-t}}{2} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 28

DSolve[{D[x[t],{t,2}]+4*D[x[t],t]+3*x[t]==1,{x[0]==0,Derivative[1][x][0] ==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{6} e^{-3 t} \left (e^t-1\right )^2 \left (2 e^t+1\right ) \]