DE of a family of straight lines

1. A.
   $y = (x - 1)\frac{dy}{\text{ }dx} - 1$
2. B.
   $\ x = (x - 1)\frac{dy}{\text{ }dx} + 1$
3. C.
   $y = (x - 1)\frac{dy}{\text{ }dx}$
4. D.
   $\ y = 2(x - 1)\frac{dy}{\text{ }dx}$

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1. A.
   $\dfrac{d^2y}{dx^2} = 0$
2. B.
   $\dfrac{dy}{dx} = 0$
3. C.
   $\dfrac{dy}{dx} = -\cot\alpha$
4. D.
   $\dfrac{d^2y}{dx^2} = \csc^2\alpha$

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1. A.
   $\left(x - y\dfrac{dy}{dx}\right)^2 = 1 + \left(\dfrac{dy}{dx}\right)^2$
2. B.
   $\left(y - x\dfrac{dy}{dx}\right)^2 = 1 + \left(\dfrac{dy}{dx}\right)^2$
3. C.
   $\left(x + y\dfrac{dy}{dx}\right)^2 = 1 + \left(\dfrac{dy}{dx}\right)^2$
4. D.
   $\left(y + x\dfrac{dy}{dx}\right)^2 = 1 + \left(\dfrac{dy}{dx}\right)^2$

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1. A.
   $\dfrac{dy}{dx} + \sqrt{3} = 0$
2. B.
   $\dfrac{dy}{dx} + 1 = 0$
3. C.
   $dx + \sqrt{3}\,dy = 0$
4. D.
   $\dfrac{dy}{dx} = 0$

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