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

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

\[ \left[1 + \left(\frac{dy}{dx}\right)^2 \right]^{3/2} = \frac{d^2 y}{dx^2} \]

is ______.

The number of solutions of \( \frac{dy}{dx} = y^{1/3} \) passing through origin is
The order and degree of the differential equation \( (y'')^2 + (y''')^3 - (y')^4 + y^5 = 0 \) is
The order and degree of the differential equation \( (y'')^2 + (y''')^3 - (y')^4 + y^5 = 0 \) is
The order and degree of the differential equation \( (y'')^2 + (y''')^3 - (y')^4 + y^5 = 0 \) is
The order and degree of the differential equation \( (y'')^2 + (y''')^3 - (y')^4 + y^5 = 0 \) is
The order of the differential equation \( \left(\frac{d^3y}{dx^3}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^5 = 0 \) is:
The differential equation representing the family of curves $y^2 = a(ax + b)$ where $a$ and $b$ are arbitrary constants, is of:
The order and degree of the differential equation

\[ \left[2\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 \right]^{\frac{3}{2}} = \frac{d^3y}{dx^3} \]

The solution of the differential equation \( \frac{dy}{dx} = e^x + 1 \) is:
The solution of the differential equation \( \frac{dy}{dx} = e^x + 1 \) is:
The solution of the differential equation \( \frac{dy}{dx} = e^x + 1 \) is: