Internal problem ID [4654]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+5 x^{\prime }+6 x-\cos \relax (t )=0} \end {gather*} With initial conditions \begin {align*} \left [x \relax (0) = {\frac {1}{10}}, x^{\prime }\relax (0) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.032 (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)
\[ x \relax (t ) = \frac {{\mathrm e}^{-3 t}}{10}-\frac {{\mathrm e}^{-2 t}}{10}+\frac {\cos \relax (t )}{10}+\frac {\sin \relax (t )}{10} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 26
DSolve[{x''[t]+5*x'[t]+6*x[t]==Cos[t],{x[0]==1/10,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{10} \left (e^{-3 t}-e^{-2 t}+\sin (t)+\cos (t)\right ) \\ \end{align*}