38.4.19 problem 20

Internal problem ID [6505]
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 : 20
Date solved : Monday, January 27, 2025 at 02:09:28 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+5 x^{\prime }+6 x&=\cos \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&={\frac {1}{10}}\\ x^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 25

dsolve([diff(x(t),t$2)+5*diff(x(t),t)+6*x(t)=cos(t),x(0) = 1/10, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {{\mathrm e}^{-3 t}}{10}-\frac {{\mathrm e}^{-2 t}}{10}+\frac {\cos \left (t \right )}{10}+\frac {\sin \left (t \right )}{10} \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 26

DSolve[{D[x[t],{t,2}]+5*D[x[t],t]+6*x[t]==Cos[t],{x[0]==1/10,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{10} \left (e^{-3 t}-e^{-2 t}+\sin (t)+\cos (t)\right ) \]