Math 293 solution set 9 - Math 293 Solutions to Problem Set...

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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
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