Form the DE by eliminating arbitrary constants from a given equation

1. A.
   $\left(\frac{dy}{dx}\right)^3=27y$
2. B.
   $\left(\frac{dy}{dx}\right)^3=-27y$
3. C.
   $8\left(\frac{dy}{dx}\right)^3=27y$
4. D.
   $8\left(\frac{dy}{dx}\right)^3+27y=0$

Tap an option to check your answer.

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

Tap an option to check your answer.

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

Tap an option to check your answer.

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

Tap an option to check your answer.

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

Tap an option to check your answer.

1. A.
   $\frac{d^{2}y}{{dt}^{2}} + 6y = 0$
2. B.
   $\frac{d^{2}y}{{dt}^{2}} = 0$
3. C.
   $\frac{d^{2}y}{{dt}^{2}} + 36y = 0$
4. D.
   $\frac{d^{2}y}{{dt}^{2}} + 25y = 0$

Tap an option to check your answer.

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

Tap an option to check your answer.

1. A.
   $y^{''} = y'y$
2. B.
   $yy^{''} = y'$
3. C.
   $yy^{''} = \left( y' \right)^{2}$
4. D.
   $y' = y^{2}$

Tap an option to check your answer.

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

Tap an option to check your answer.

1. A.
   $\dfrac{dy}{dx} = \dfrac{1}{9y^2}$
2. B.
   $\dfrac{dy}{dx} = \dfrac{1}{27y^2}$
3. C.
   $\dfrac{dy}{dx} = \dfrac{1}{81y^2}$
4. D.
   $\dfrac{dy}{dx} = \dfrac{1}{36y^2}$

Tap an option to check your answer.

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

Tap an option to check your answer.

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

Tap an option to check your answer.