List of top Mathematics Questions on Order and Degree of Differential Equation asked in MHT CET

The order and degree of the differential equation $e^{\frac{dy}{dx}}+\frac{dy}{dx}=x$ is

The order of the differential equation representing the family of all parabolas having a fixed latus rectum of length $4a$ and an axis parallel to the x-axis is...

The order and degree of the differential equation $\sqrt{⎷1+\frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}$, respectively are

The order and degree of the differential equation $(\frac{d^3y}{dx^3})^{\frac{2}{3}}-3\frac{d^2y}{dx^2}+5\frac{dy}{dx}+4 = 0$ are respectively

The order and degree of the differential equation $\sqrt{⎷1+\frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{\frac{3}{2}}$ are $\ldots$

The area of the region bounded by curves $y = sinx,y = cosx$ and the lines $x = 0$, $x = \frac{π}{4}$ is

For the differential equation $\frac{d^3y}{dx^3}+cos(\frac{d^2y}{dx^2}) = 0$, which of the following is true ?

The degree of the differential equation obtained from the equation $(y-a)^2 = 4(x-b)$ [where $a$ and b are arbitrary constants] is

The order and degree of the differential equation $3-(\frac{\text{d}^3y}{\text{d}x^3})^{\frac{7}{3}} = (\frac{\text{d}y}{\text{d}x})^5$ are respectively

The order and degree of the differential equation $\sqrt{2+(\frac{d^2y}{dx^2})^3} = (\frac{d^3y}{dx^3})^{5/2}$ respectively are

What is the order of the differential equation $ \dfrac{d^2 y}{dx^2} + \left(\dfrac{dy}{dx}\right)^3 = 0 $?

The order and degree of the differential equation $\sqrt{\frac{\mathrm{d} y}{\mathrm{~d} x}}-4 \frac{\mathrm{~d} y}{\mathrm{~d} x}-7 x=0$ is respectively

The order of the differential equation whose general solution is given by $y = (C_1 + C_2) \sin(x + C_3) - C_4 e^{x+C_5}$ is \dots}

The degree of the differential equation $\frac{d^2y}{dx^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log \left( \frac{d^2y}{dx^2} \right)$ is

The differential equation representing the family of curves $y^2 = 2c(x + \sqrt{c})$, where $c$ is a positive parameter, is of}

The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is

The degree of the differential equation whose solution is $y^2 = 8a(x+a)$, is

The order and degree of the differential equation $$\frac{d^2y}{dx^2} = \sqrt{\frac{dy}{dx}}$$ are respectively

The order of the differential equation whose solution is $y = a \cos x + b \sin x + c e^{-x}$ is

If $ m $ is order and $ n $ is degree of the differential equation \[ \left( \frac{d^2y}{dx^2} \right)^5 + 4 \left( \frac{\frac{d^2y}{dx^2}}{\frac{d^3y}{dx^3}} \right) + \left( \frac{d^3y}{dx^3} \right) = x^2 \] then

If $m$ is order and $n$ is degree of the differential equation $y = x\frac{dy}{dx} + \sqrt{a^2 \left(\frac{dy}{dx}\right)^2 - b^2}$, then the value of $m + n$ is

The differential equation of family of circles whose centres lie on X-axis is

The differential equation of $y = e^x (a \cos x + b \sin x)$ is