Math 293 Solutions to Problem Set 9. § 1.3 #12 . dy dx = y . The isoclines are obtained by setting dy dx equal to a constant c , the slope of the slope-indicator line segments all along the isocline. In the present case the isoclines are the horizontal lines y = c , light red in the ﬁgure (if you’re able to view the ﬁgure in color). Some solutions are drawn in blue. The one passing through (0 ,-1) satisﬁes the initial condition y (0) =-1. We can solve the equation dy dx = y explicitly by separating variables to get y-1 dy = dx . Integration then gives the solutions y = Ce x . The graphs of these functions are the blue curves in the picture. #13 . dy dx =-x y . The isoclines are the curves-x y = c ,or
This is the end of the preview. Sign up
access the rest of the document.
This homework help was uploaded on 01/21/2008 for the course MATH 2930 taught by Professor Terrell,r during the Spring '07 term at Cornell University (Engineering School).