MATH 024 Study Guide - Final Guide: Mechanical Equilibrium, Saddle Point, Main Diagonal
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Lecturer: boaz ilan: consider the differential equation (de) dy dt y(2 y ) Solution: initial conditions y(0) = 1and y(0) = 3. y(0) = 1? (a) this de is 1st order, nonlinear, autonomous, and separable (b) dy dt y(2 y ) = 0 y = 0 & y = 2are the equilibrium solutions. (c) a direction field has been plotted below. Ty = e (a) find the integrating factor. (b) find the general solution. 3 (a) (t) = e (b) multiply both sides by the integrating factor. = e a perfect derivative of the integrating factor and y. Now we can explicitly solve for y to get: let. = (t + c )e t + c. 0 4 (b) since the determinant of a is not zero, a is invertible. Therefore, ax = 0 has only the trivial solution x = 0. method to determine the rref of a.
