What are the order and the degree respectively of the differential equation x^{2}\left(\frac{d^{3}y}{dx^{3}}\right)^{2}+\left(\frac{dy}{dx}\right)^{4}+\sin x=0?

Explanation

The order of a differential equation is the order of the highest derivative present, which is 3 (from \frac{d^3y}{dx^3}). The degree is the highest power of the highest order derivative when the equation is a polynomial in derivatives. The power of \frac{d^3y}{dx^3} is 2. Hence, the order is 3 and the degree is 2.

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