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Use the direction field labeled III (above) to sketch the graphs of the solutions that satisfy the given initial conditions.(a) $y(0)=1$(b) $y(0)=2.5$(c) $y(0)-3.5$

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a) To sketch the graph of the solution that satisfy $y(0)=1$D E p \operatorname{lot}(O D E I, y(x),-2 \ldots 2,[y(0)=1],$ linecolor $=\operatorname{green},$ color $=$ blue, arrows $=L I N E)$b)To sketch the graph of the solution that satisfy $y(0)=2.5$$D E p \operatorname{lot}(O D E I, y(x),-2 \ldots 2,[y(0)=2.5],$ linecolor $=$ green, color $=$ blue, arrows $=L I N E)$c)To sketch the graph of the solution that satisfy y $(0)=3.5 :$DEplot $(O D E I, y(x),-2 \ldots 2,[y(0)=3.5],$ linecolor $=$ green, color $=$ blue, arrows $=L I N E)$

Calculus 2 / BC

Chapter 9

Differential Equations

Section 2

Direction Fields and Euler's Method

Oregon State University

Harvey Mudd College

Idaho State University

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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they're given a slope. It's an initial condition. You're asked to find a solution Satisfying over is and important day for condition. What we're given Why? You know, one I'll throw this crap So they have 101 You can see by following slopes their lowest possible, uh, coaches Positive infinity. Yeah. Why also Urges more look like something with her life support. And he asked on the solution. The initial condition y zero equals equals five. This is great. Really happened here. 25 and we follow. This is nearly as possible. We get that graph search is asking the ground. What? This is something like a reflection of on a first draft across the s and take life too. I'm going. Attraction. Political gin Report seen. He has to find a solution. Initial condition wise, dear Rose 3.5 Practice green that we have here five all slopes. I feel that it's possible to get that. Yeah, Why the end? So you see, we have looks like stretch off previous graph again A reflection of the first draft, the s and fight

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