38.4.16 problem 17

Internal problem ID [6502]
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 : 17
Date solved : Monday, January 27, 2025 at 02:09:10 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=85 \sin \left (3 t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=-20 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 31

dsolve([diff(x(t),t$2)+2*diff(x(t),t)+2*x(t)=85*sin(3*t),x(0) = 0, D(x)(0) = -20],x(t), singsol=all)
 

\[ x \left (t \right ) = \left (7 \sin \left (t \right )+6 \cos \left (t \right )\right ) {\mathrm e}^{-t}-6 \cos \left (3 t \right )-7 \sin \left (3 t \right ) \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 36

DSolve[{D[x[t],{t,2}]+2*D[x[t],t]+2*x[t]==85*Sin[3*t],{x[0]==0,Derivative[1][x][0 ]==-20}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 7 e^{-t} \sin (t)-7 \sin (3 t)+6 e^{-t} \cos (t)-6 \cos (3 t) \]