MATH 223 Lecture Notes - Lecture 3: Angular Frequency, Simple Harmonic Motion, Damping Ratio
21 Oct 2020
School
Department
Course
Professor
Document Summary
Determine the general solution of the following ivps. If we consider the homogeneous ode, we have y + 2y 15y = 0. The characteristic equation is m2 + 2m 15 = (m + 5)(m 3) = 0. Therefore, the characteristic roots are m = 5 and m = 3. The general solution to the homogeneous ode is thus: yh (x) = ae 5x + be3x. The right hand side of the original ode is f (x) = x. Thus the particular solution is of the form yp (x) + x. Di erentiating yp (x) and substituting back into the ode, we get = 1. 15 and y(x) = ae 5x + be3x . 15 x: a) for the initial conditions y(0) = 2 equations in a and b: 225 and y (0) = 0, we get the following system of which yields a = 1. 15 x: b) for the initial conditions y(1) = 2.
