MATH 1005 Study Guide - Final Guide: Integrating Factor, Single-Photon Emission Computed Tomography, Partial Derivative

• School: Carleton University
• Department: Mathematics
• Course: MATH 1005
• Professor: Zahra Montazeri

Document Summary

Separable equations have the form g(y)y0 = f (x). To solve, we integrate both sides with respect to x and use the substitution rule on the left to get. We carry out the integration and can then solve for y (if possible). Homogeneous equations have the form y0 = f y x . To solve, we make the substitution u = y: then y = xu and so y0 = u + xu0. Replac- ing each occurrence of y x with u and the y0 with u + xu0 will result in a di erential equation (in u) which is guaranteed to be separable (after rearranging). Once we have u, we use y = xu to nd y. Linear equations have the form a(x)y0 + b(x)y = c(x). Dividing by a(x) yields the standard form: y0 + p (x)y = q(x).