MATH 133A San Jose State

Math 133A Essentials I. Basic notions. Solutions (explicit and implicit), initial value problems (IVPs) Existence and uniqueness theorem Direction elds II. First order equations. Methods for solving: Separable equations y = u(x)v(y) Linear equat

San Jose State University Math 133A, Fall 2004 Quiz 6 Solve the given initial value problem: y 2y + 2y = 0, y() = e , y () = 0. Solution: The associated characteristic equation is r2 2r + 2 = 0. Its roots are 1 i, so the general solution is y

San Jose State University Math 133A, Fall 2004 Quiz 8 Determine the inverse Laplace transform of the given function: 3 . (2s + 5)3 Solution: Using L{tn }(s) = n!/sn+1 with n = 2 and L{eat f (t)}(s) = L{f }(sa), we obtain L1 3 (2s + 5)3 (t) = 3 1 2

San Jose State University Math 133A, Fall 2005 Quiz 1 Solution Solve the given initial value problem: dy t2 = , dt y + t3 y y(0) = 2. Solution: Separating the variables and integrating, we obtain ydy = t2 dt. 1 + t3 The right-hand side can be so