Learning Guide Learning Guide

238 • Chapter 6: Examples from CalculusYou can also do the two steps at once.> y[2] := unapply( eval( x[2](t), ans ), t );y 2 := t → 50121( 1110 t2 + 910 − 11 5 t + 1 5 cosh( 1 √ √−11 100 (t − 1)))10Heaviside(t − 1) + 2 11 − 2 11 cosh( 1 10√ −11√100 t)Now plot the two functions.> plot( [ y[1](t), y[2](t) ], t=-3..6 );1412108642–2 2 4 6tInstead of using dsolve(..., method=laplace), you can use theLaplace transform method by hand. The inttrans package defines theLaplace transform and its inverse (and many other integral transforms).> with(inttrans);[addtable, fourier, fouriercos, fouriersin, hankel , hilbert,invfourier, invhilbert, invlaplace, invmellin, laplace,mellin, savetable]The Laplace transforms of the two differential equations eqn1 andeqn2 are> laplace( eqn1, t, s );α m (s (s laplace(x 1 (t), t, s) − x 1 (0)) − D(x 1 )(0)) =k (laplace(x 2 (t), t, s) − laplace(x 1 (t), t, s)) + e(−s)s