Maple 9 Learning Guide - Maplesoft

7.2 Ordinary Differential Equations • 247> laplace( eqn2, t, s );m (s 2 laplace(x 2 (t), t, s) − D(x 2 )(0) − s x 2 (0)) =k (laplace(x 1 (t), t, s) − laplace(x 2 (t), t, s))Evaluate the set consisting of the two transforms at the initial conditions.> eval( {%, %%}, {ini} );{α m (s 2 laplace(x 1 (t), t, s) − 2 s) =k (laplace(x 2 (t), t, s) − laplace(x 1 (t), t, s)) + e(−s)s ,m s 2 laplace(x 2 (t), t, s) =k (laplace(x 1 (t), t, s) − laplace(x 2 (t), t, s))}You must solve this set of algebraic equations for the Laplace transformsof the two functions x 1 (t) and x 2 (t).> sol := solve( %, { laplace(x[1](t),t,s),> laplace(x[2](t),t,s) } );sol := {laplace(x 1 (t), t, s) = (m s2 + k) (2 α m s 2 e s + 1)e s s 3 m (k + α m s 2 + α k) ,laplace(x 2 (t), t, s) =k (2 α m s 2 e s + 1)e s s 3 m (k + α m s 2 + α k) }Maple has solved the algebraic problem. You must take the inverseLaplace transform to get the functions x 1 (t) and x 2 (t) .> invlaplace( %, s, t );