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A direction field for the differential equation $ y^1 = x \sin y $ is shown.(a) Sketch the graphs of the solutions that satisfy the given initial conditions.(i) $y(0)=1$(ii) $y(0)=0.2$(iii) $y(0)=2$(iv) $y(1)=3$(b) Find all the equilibrium solutions.
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Calculus 2 / BC
Direction Fields and Euler's Method
Missouri State University
University of Nottingham
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.
A direction field for the …
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