Differential equation of a family of curves: eliminate the constants

1. A.
   $y\left( \frac{dy}{dx} \right)^{2} - 2x\left( \frac{dy}{dx} \right) - y = 0$
2. B.
   $y\left( \frac{dy}{dx} \right)^{2} - 2x\left( \frac{dy}{dx} \right) + y = 0$
3. C.
   $y\left( \frac{dy}{dx} \right)^{2} + 2x\left( \frac{dy}{dx} \right) - y = 0$
4. D.
   $y\left( \frac{dy}{dx} \right) + 2x\left( \frac{dy}{dx} \right) - y = 0$

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1. A.
   $10\frac{d^{2}y}{dx^{2}} = 11$
2. B.
   $11\frac{d^{2}x}{dy^{2}} = 10$
3. C.
   $10\frac{d^{2}x}{dy^{2}} = 11$
4. D.
   $11\frac{d^{2}y}{dx^{2}} = 10$

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1. A.
   $2xy\frac{dy}{dx} + \left( x^{2} - y^{2} + 4 \right) = 0$
2. B.
   $2xy\frac{dy}{dx} + \left( x^{2} + y^{2} - 4 \right) = 0$
3. C.
   $2xy\frac{dy}{dx} + \left( y^{2} - x^{2} + 4 \right) = 0$
4. D.
   $2xy\frac{dy}{dx} - \left( x^{2} - y^{2} + 4 \right) = 0$

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

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