The integrating factor of the differential equation $\cos x \frac{dy}{dx} + y\sin x = 1$ is

The general solution of the differential equation $\frac{dy}{dx}-\frac{y}{x}+\text{cosec}\left(\frac{y}{x}\right)=0$ is

(Consider $\log x=\log_e x$)

In the following differential equation $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 = 2x^2 \log\left(\frac{d^2y}{dx^2}\right)$ order and degree is:

Solution of differential equation $x dy - y dx = 0$ respresents :

The solution of the differential equation $\frac{dy}{dx} = \frac{6}{x^2}$; $y(1) = 3$ is :

General solution of the differential equation $(e^x + e^{-x})dy = (3e^{2x} + 3e^{4x})dx$ is:

[Where C is an arbitrary constant]

The solution of the differential equation $x\frac{dy}{dx} = 2x^2 + 1$; $x \neq 0$ with $y = 1$ when $x = 1$, is