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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.

A. $ y^{'} = 1 + xy $B. $ y^{'} = -2 xy $C. $ y^{'} = 1 - 2xy $

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Equation $C$

Calculus 2 / BC

Chapter 9

Differential Equations

Section 1

Modeling with Differential Equations

Harvey Mudd College

Baylor University

Boston College

Lectures

13:37

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

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So today I'm going to show you how to choose. Select the graft off the solution for the differential equation. So first thing I will let you know. So this one is a differential equation. It's different than the calculus one. So in calculus one, we have white pine equal to something here. Some function off X Here is the only variable here, but in the differential equation we have the Y and X. So it's different. So in this one, a little bit tricky When we take a B c So we found be Maybe it's the easiest way The easiest way to start here because we knew when x let because an zero Why Big 10, 0 plus and zero We get this whole turned white point should be negative. So doesn't feed. And here for a because they have one here. If we choose the domain here ex Lattanzio why Lattanzio we get why Pine in First Squadron, It's Luxan zero. It doesn't fit also. So here is the only one. See so things because we have no idea for the for the sea Here it's minus. And here it's one we don't know on First Squadron is large or small or what house we can think. Maybe the second quadrant and third quadrant. Maybe we can think so. We can. We also cannot think for Maybe we can think the second quadrant. Yeah, its feet for this glass.

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