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

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

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