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Direction Fields | Differential Equations | Mathematics | MIT OpenCourseWare

Direction Fields | Differential Equations | Mathematics | MIT OpenCourseWare

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SOLVED:draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t →∞. If this behavior depends on the initial value of y at t=0, describe this dependency. Note that in these problems the equations are not of the form y^'=a y b and the behavior of their solutions is somewhat more complicated than for the equations in the text. y^'=y(4-y)

SOLVED:draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t →∞. If this behavior depends on the initial value of y at t=0, describe this dependency. Note that in these problems the equations are not of the form y^'=a y b and the behavior of their solutions is somewhat more complicated than for the equations in the text. y^'=y(4-y)

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SOLVED:draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t →∞. If this behavior depends on the initial value of y at t=0, describe this dependency. Note that in these problems the equations are not of the form y^'=a y b and the behavior of their solutions is somewhat more complicated than for the equations in the text. y^'=y(4-y)

SOLVED:draw a direction field for the given differential equation. Ba…

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