List of top Higher Mathematics Questions on Differential Equations

Order of differential equation \( xy \frac{d^2y}{dx^2} + x \left( \frac{dy}{dx} \right)^2 - y \frac{dy}{dx} = 0 \) is 2.

Find the general solution of the differential equation \[ x \frac{dy}{dx} + 2y = x^2 \,\,\, \text{where} \,\,\, (x \neq 0). \]

Find the general solution of the differential equation \[ \frac{dy}{dx} = \frac{1 + y^2}{1 + x^2}. \]
Integrating factor of differential equation \( \frac{dy}{dx} - y = \cos x \) is \( e^{-x} \).
The number of arbitrary constants in the particular solution of a differential equation of third order are \(\underline{\hspace{2cm}}\)