Answer Happy

* = 1. * You should answer part of this question in the group quiz. (L) Find the homogeneous solution of the ODE day dy -6 +9y = r(x). d.x2 dr For each of the following functions r(x), write down an appropriate guess for yp(2) (a) (L) r(x) = 2 + 3x + 6e-* (b) (L) r(x) = r sin(2) (c) (T) r(2) = 6xe3r. For this case, also find the particular solution. This one is tricky - think carefully about your guess. 2. * You should answer part of this question in the group quiz. (L+) Find the solution of the ODE y" - y' – 2y = 0 that satisfies y(0) = 1 and y is bounded (its magnitude stays less than a finite value) as 2 + 0. y 3. * You should answer part of this question in the group quiz. (L) The general solution of the ODE y" – 7y' +12y = -24 is y(x) = Ae3x + Be4r – 2. Find the solution satisfying the initial conditions y0) = 1 and y'(0) = 1. 4. * You should answer part of this question in the group quiz. (T) The general solution of an ODE is y(x) = Ae" + Be2x + x2 What is the ODE that this solution satisfies, given that the coefficient for day/dx2 is 1? * = =