DE of a family of circles

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

Tap an option to check your answer.

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

Tap an option to check your answer.

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

Tap an option to check your answer.

1. A.
   $(5 - y)\frac{dy}{\text{ }dx} + y^{2} - 10y = 0$
2. B.
   $\ (5 - y)^{2}\frac{{\text{ }d}^{2}y}{\text{ }dx^{2}} + y^{2} - 10y = 0$
3. C.
   $\ (5 - y)\frac{dy}{\text{ }dx} + y - 10 = 0$
4. D.
   $\ (5 - y)^{2}\left( \frac{\text{ }dy}{\text{ }dx} \right)^{2} + y^{2} - 10y = 0$

Tap an option to check your answer.

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

Tap an option to check your answer.

1. A.
   $\dfrac{dy}{dx} = \dfrac{x - 1}{x - 2}$
2. B.
   $\dfrac{dy}{dx} = \dfrac{x - 1}{2 - x}$
3. C.
   $\dfrac{dy}{dx} = \dfrac{1 - x}{2 - y}$
4. D.
   $\dfrac{dy}{dx} = \dfrac{1 - x}{y - 2}$

Tap an option to check your answer.

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

Tap an option to check your answer.