MATH 215 Study Guide - Midterm Guide: Phase Portrait
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Solve the initial value problem: dy dx ey x + 2 y(0) = 0, x 0. Also, determine the largest interval of positive x where this solution exists. Determine if the following equation is exact or not, and in either case, nd the general solution: ydx + (x2y x)dy = 0, x > 0. Let < y0 < and consider the following initial value problem: dy dt. Each of the following four pictures are phase portraits of the system of. = ax, where a is a constant, 2 2 matrix. For each picture, check the appropriate equations x boxes to indicate the properties of the eigenvalues of a. In the blank, indicate the sign (positive, negative, or zero) of each eigenvalue (or of its real part). For the two pictures below, check the appropriate boxes to indicate the properties of the eigenvalues of a.
