Quiz 1 for Mathematics 3113-005: Solutions to Differential Equations and Integrals - Prof., Quizzes of Mathematics

Download Quiz 1 for Mathematics 3113-005: Solutions to Differential Equations and Integrals - Prof. and more Quizzes Mathematics in PDF only on Docsity! Mathematics 3113-005 Quiz 1 Form A January 28, 2011 Name (please print) Instructions: Give concise answers, but clearly indicate your reasoning. Most of the problems have rather short answers, so if you find yourself involved in a lengthy calculation, it might be a good idea to move on and come back to that problem if you have time. I. (3) Find infinitely many solutions of the differential equation 5y′ = 3y. Start by looking for a solution of the form y = erx, where r is a certain constant. II. (2) Tell two well-known basic functions that are solutions of y′′ = −y. III. (5) (a) Solve the initial value problem dy dx = 3 x4 , y(2) = 0. (b) Apply the Existence and Uniqueness Theorem to this initial value problem (that is, verify that this initial value problem satisfies the hypotheses of the theorem). What does the theorem tell you about the solution you have found? IV. (3) The separable differential equation dy dx = x2 y can be writtten as y dy = x2 dx. Integrate both sides of this and solve for y to find the general solution. V. (2) What basic types of mathematical objects (more basic than “integral”) appear on the two sides of this well-known equation: ∫ cos(x) dx = sin(x) + C?