Internal problem ID [4651]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+2 x^{\prime }+2 x-85 \sin \left (3 t \right )=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 0, x^{\prime }\relax (0) = -20] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ x \relax (t ) = \left (7 \sin \relax (t )+6 \cos \relax (t )\right ) {\mathrm e}^{-t}-6 \cos \left (3 t \right )-7 \sin \left (3 t \right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 33
DSolve[{x''[t]+2*x'[t]+2*x[t]==85*Sin[3*t],{x[0]==0,x'[0]==-20}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -7 \sin (3 t)-6 \cos (3 t)+e^{-t} (7 \sin (t)+6 \cos (t)) \\ \end{align*}