The sum of order and degree of the differential equation $\frac{\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{\frac{5}{2}}}{\frac{d^2y}{dx^2}} = p$ is :

The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{x^2+xy+y^2}{x^2}$ for $x>0, y>0$ at $x=1, y=2$ is

Integrating factor of the differential equation $\frac{dy}{dx} - \frac{1}{x} y = 1$ is:

The integrating factor of the differential equation $\frac{dy}{dx} = x + xy$ is

Solution of differential equation $\frac{dy}{dx} = \frac{1+x^2}{1+y^2}$ is

If $\sin y=x \sin (a+y)$, then $\frac{d y}{d x}$ is :

Which of the following differential equations has $y = x$ as one of its particular solution?