List of top Mathematics Questions on Order and Degree of Differential Equation

The order and degree of differential equation (d²y/dx²)³ + (dy/dx)² + y = 0 respectively

The order and degree of the differential equation \[ \left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{3/2} = \frac{d^2y}{dx^2} \] are respectively

If \(a,b\) are arbitrary constants, then the differential equation corresponding to family \[ y=ax^2-2abx+ab^2 \] is

The order and degree of the differential equation $\left[1 + \left(\frac{dy}{dx}\right)^2\right]^{3/2} = \frac{d^2y}{dx^2}$ are respectively:

The order and degree of the differential equation \[ \left(\frac{d^2y}{dx^2}\right)^3+\left(\frac{dy}{dx}\right)^2+y=0 \] are respectively:

The degree of the differential equation \[ \sqrt{1+\left(\frac{dy}{dx}\right)^{1/3}}=\frac{d^2y}{dx^2} \] is:

If \( \dfrac{d^2y}{dx^2} = \cos \left(\dfrac{dy}{dx}\right) \), find the order and the degree of the resulting differential equation.

The order and the degree of the differential equation $2\frac{dy}{dx}-3x=\left(2y-x\frac{dy}{dx}\right)^{-3}$ respectively, are

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

The elimination of arbitrary constants $c_{1}, c_{2}, c_{3}, c_{4}$ from $y=(c_{1}+c_{2})\sin(2x+c_{3}) + c_{4}e^{5x}$ gives a differential equation of order ________.

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 elimination of arbitrary constants $c_{1}, c_{2}, c_{3}, c_{4}$ from $y=(c_{1}+c_{2})\sin(x+c_{3})-c_{4}e^{x}$ gives a differential equation of order:

The degree of the differential equation \( \int \frac{x}{(x-1)(x-2)^2} dx = a \log \left| \frac{x-1}{x-2} \right| + \frac{b}{x-2} + c \) is:

The degree of the differential equation \[ \left( 1 + \left( \frac{dy}{dx} \right)^2 \right)^{\frac{3}{4}} = \left( \frac{d^2y}{dx^2} \right)^{\frac{1}{3}} \]

The order of the differential equation \( \frac{d}{dz}\left[\left(\frac{dy}{dz}\right)^3\right]=0 \) is

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

\(p\) and \(q\) are positive integers and \(n\lt r\lt m\). If the order and degree of the differential equation \[ \left( \frac{d^my}{dx^m}+\frac{d^ny}{dx^n} \right)^{p/q} = 5\frac{d^ry}{dx^r} \] are respectively \(4\) and \(3\), then

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