Question

Page 2 II. (7) Use the Laplace Transform method to solve the IVP y' - 8y + 16y = 14 y(0) = 1,5/(0) = 4 Show all your work. Note: A partial fraction decomposition will not be needed here if you carefully solve for Y (s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the coefficient of Y(s) which will be of the form 52 -2m8+m2 (s - m). At this time, check your work by verifying that Y(s) is of the form + (8 - m) * (8 - m) and proceed to find the solution to the IVP by computing the inverse Laplace transform of Y(s). a b

Answer 1

(. به سه رواه = (ہ) کھا لا ،) + و - لا Apply Laplace Transform on bonsidy 2 کا = {لا ، رعایا و رو( ) = (2) .را وا+( او )ا - (ا )L =(9) کا +ژه) 9 - (واده - 9- ما وو- (9)ی ترکی) 4- (0) - (1ء فرها- 2 = ها+ - (L9 (556) فرهی (وا (+) 2 = ریا - دری -85 Lly)+801) +16L(y) 2 2 (Saqats-4 ts) 2 s/ (egg s-4 Apply Invesse Laplace Transform, + + کرم کا = 3ر276 ا} + تره { } +ره کا 2 =الا = ره) 9 ت 2 + 1 4. "(t) = t ettetett