The order and degree of the differential equation ${[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)]}^{3/4}=\frac{d^{2}y}{d{x}^2}$ are:

The correct option is D order$=2$; degree $=$ not defined
We have, ${[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)]}^{3/4}=\frac{d^{2}y}{d{x}^2}$

Take forth power both sides,

${[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)]}^3={\left(\frac{d^{2}y}{d{x}^2}\right)}^4$

Clearly above differential equation is not a polynomial equation in differential coefficient

Hence degree is not defined

But the order is the highest order of differential term which is $2$ here.