Determine the order and degree (if defined) of the differential equation $y'' + (y')^2 + 2y = 0$.

The order and degree of the differential equation $\left[1+\frac{1}{(\frac{dy}{dx})^{2}}\right]^{\frac{5}{3}}=5 \frac{d^{2}y}{dx^{2}}$ are respectively:

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

If $m$ is the order and $n$ is the degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^5+4 \frac{\left(\frac{d^2 y}{d x^2}\right)}{\left(\frac{d^3 y}{d x^3}\right)}+\left(\frac{d^3 y}{d x^3}\right)=x^2-1$,then:

The degree of the differential equation $\frac{d^2y}{dx^2} - \sqrt{\frac{dy}{dx} - 3} = x$ is

Find the sum of the order and degree of the differential equation $y = x(\frac{dy}{dx})^3 + \frac{d^2y}{dx^2}$.