Determine the order and degree (if defined) of the differential equation $y^{\prime} + y = e^{x}$.

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

The differential equation representing the family of curves ${y^2} = 2c(x + \sqrt{c}),$ where $c$ is a positive parameter,is of

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 $\sqrt{1 + (\frac{d^2y}{dx^2})^2} = \sqrt[3]{x + (\frac{dy}{dx})^3}$ are respectively . . . . . . and . . . . . . .

The degree of the differential equation $\left( \frac{d^3y}{dx^3} \right)^2 + 4\left( \frac{dy}{dx} \right)^3 = 3\sin \left( \frac{d^2y}{dx^2} \right)$ is: