The function with the given graph is a solution of one of th

The function with the given graph is a solution of one of the following differential equations. Decide which is the correct equation and justify your answer. y\' = 1 + xy y\' = -2xy y\' = 1 - 2xy

Solution

The answer is C.

Since we know that y\' = 1 + xy, we know the slope of the tangent line at any point.

At x = 0, y > 0 (in the graph shown). We also know that at x = 0, the tangent line has a slope that is postive. If we plug this information into A or C, we get a postitve value for y \'. However, B gives you a negative answer for y \'. In addtion, we know that the slope of the tangent line eventually becomes negative and then becomes postive again. For A, this is not possible (y\' just keeps on increasing). Therefore, the only option we have left is C.