Learning Guide Learning Guide

250 • Chapter 6: Examples from CalculusYou can now plot the response.> plot(p, t=0..30);100806040200–205 10 15 20 25 30tThis particular example has the following analytic solution.> dsolve( {eq(t), ini}, {theta(t)} );θ(t) = 20 + 80 e(−1/10 t)> q := rhs(%);q := 20 + 80 e(−1/10 t)Thus, you can compare the series solution with the actual solution.> plot( [p, q], t=0..30 );100806040200–205 10 15 20 25 30tInstead of finding the Taylor series by hand, you can use the seriesoption of the dsolve command.> dsolve( {eq(t), ini}, {theta(t)}, ’series’ );