MAT 221B Final: Math 22B Final Exam Spring 2017
Document Summary
Sample final questions: (a) solve the following initial value problem for y(x) in x > 0: y . < x < + : (a) find a particular solution of the ode xy + y = x3. Try a solution of the form y(x) = ax3 + bx2 + cx. (b) use general theorems to explain why there are unique, linearly indepen- dent solutions y1(x), y2(x) of the following initial-value problems xy xy . 2 + y2 = 0, y1(1) = 1, y2(1) = 0, y . 1: (a) find the general solution of the equation y + y . Y = g(x), y(0) = 0, y (0) = 0, where g(x) is a given continuous function. (a) write y(x) = exu1(x) + e xu2(x), where exu . Find the general solution of the ode my + cy + ky = 0. Express your answer in terms of real-valued functions.
