The order and degree of the differential equation $\frac{d^2y}{dx^2} = \left\{ y + \left( \frac{dy}{dx} \right)^2 \right\}^{1/4}$ are:

The order of the differential equation whose solution is ${x^2} + {y^2} + 2gx + 2fy + c = 0$ is:

The order and the degree of the differential equation $\frac{d^4y}{dx^4} - 4\frac{d^3y}{dx^3} + 8\frac{d^2y}{dx^2} - 8\frac{dy}{dx} + 4y = 0$ are respectively:

The order of the differential equation $y = c_{1} e^{c_{2}+x} + c_{3} e^{c_{4}+x}$ is

The number of arbitrary constants that appear in the general solution of the differential equation $\left(\frac{d^4 y}{d x^4}+\frac{d^2 y}{d x^2}\right)^{3 / 2}=5 \frac{d^3 y}{d x^3}$ is

The degree of the differential equation $\frac{d^2 y}{d x^2}+3\left(\frac{d y}{d x}\right)^2=x^2 \log \left(\frac{d^2 y}{d x^2}\right)$ is