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Use a computer algebra system to draw a direction field for the given differential equation. Ger a printout and sketch on it the solution curve that passes through (0,1). Then use the CAS to draw the solution curve and compare it with your sketch.$ y' = x^2 \sin y $

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The answer is an image of a direction field. The image and the SageMath program used to produce it are shown in the video.

Calculus 2 / BC

Chapter 9

Differential Equations

Section 2

Direction Fields and Euler's Method

Campbell University

Baylor University

University of Nottingham

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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Use a computer algebra sys…

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00:34

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Sketch the direction field…

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