38.4.13 problem 14

Internal problem ID [6499]
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 : 14
Date solved : Monday, January 27, 2025 at 02:08:57 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }-3 x^{\prime }+2 x&=\sin \left (t \right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 23

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

\[ x \left (t \right ) = \frac {{\mathrm e}^{2 t}}{5}+\frac {3 \cos \left (t \right )}{10}+\frac {\sin \left (t \right )}{10}-\frac {{\mathrm e}^{t}}{2} \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 27

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

\[ x(t)\to \frac {1}{10} \left (e^t \left (2 e^t-5\right )+\sin (t)+3 \cos (t)\right ) \]