AP Calculus AB: Differential Equations

Question

The differential equation .

1. produces a slope field with horizontal tangents at y = 2
2. produces a slope field with vertical tangents at y = 2
3. produces a slope field with columns of parallel segments

Answer Choices:

I only 

II only 

I and II 

III only

Answer 1

Jake

given dy/dx=(x-2)/(y-2)

at y=2 dy/dx→∞ which is a vertical tangent so II only is the answer.

Jim

Answer 2

We can solve this differential equation by separation to yield the following:

\frac{y^2}{2}-2y+2x-\frac{x^2}{2}=C

If we plot this and allow this constant to vary we will see that at the value y=2 the slope of the curve is always straight up or down for negative values of C.

We conclude the answer must be

(I only)

Not convinced? look for yourself

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