MATH300 Lecture 15: 15. The Laplace Equation

the table table and properties of Laplace transforms provided on the back page to Usenne the following Laplace transforms: (10 pts each) (a) S'{f'( cost. t)) where f (t)e a. (b) 묘{(1 + e-t)2 + 4t3e2t}

(1 pt) Use the Laplace transform to solve the following initial value problem: y', + 7y' = 0 y(0)--1, y'(0) = 3 First, using Y for the Laplace transform of y (t), i e , Y-L {y(t) } find the equation you get by taking the Laplace transform of the differential equation Now solve for Y(s) = -(s+6)/(s(s+7)) + st b where a

(1 pt) Find the Laplace transform of 0 t