38.4.11 problem 12

Internal problem ID [6497]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Further problems 25. page 1094
Problem number : 12
Date solved : Monday, January 27, 2025 at 02:08:45 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime }+4 x^{\prime }+3 x&={\mathrm e}^{-3 t} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&={\frac {1}{2}}\\ x^{\prime }\left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 17

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

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