List of top Mathematics Questions on General and Particular Solutions of a Differential Equation asked in BITSAT

The equation of the curve passing through the point $\left(a, -\frac{1}{a}\right)$ and satisfying the differential equation $y-x \frac{dy}{dx}=a\left(y^{2}+\frac{dy}{dx}\right)$ is

In order to solve the differential equation $x \cos x \frac{d y}{d x}+y(x \sin x+\cos x)=1$ the integrating factor is:

The solution of the differential equation $\frac{d y}{d x}+\frac{2 y x}{1+x^{2}}=\frac{1}{1+x^{22}}$ is

Given function $f(x)=\left(\frac{e^{2 x}-1}{e^{2 x}+1}\right)$ is.