Complete the following table for the differential equation dy/dx = y(1 + x)/x. C

Question

Complete the following table for the differential equation dy/dx = y(1 + x)/x. Cannot be found without solving the differential equation The differential equation dy/dx = x^2/y I. will have a slope field with positive slopes in quadrant I II. will have a slope field with negative slopes in quadrant II III. will produce a slope field with columns of parallel tangents I only II only III only None of these The slope field shown below is for the differential equation y' = 4 - 2x y' = 2x y' = y y' = x + y

Explanation / Answer

( 7 )

given

dy/dx = y ( 1 + x) / x

at x = -2 , y = -1

dy/dx = -1 ( 1 - 2 ) / -2

       ==> -1 ( -1 )/ -2

      ==> - 1/2==> - 0.5

at x = 0 ,y = 0

dy/dx = 0 ( 0 + 0 ) / 0

        = 0/ 0 ( undefined)

at x = 2 ,y = 2

dy/dx = 2 ( 1 + 2 ) / 2

        = 6 / 2

       = 3

x   - 2     0             2

y        - 1     0                 2

dy/dx   -0.5 undefined      3

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