Find the order and degree of the differential equation ${\left(\frac{d^{2}y}{d{x}^2}\right)}^3+{\left(\frac{dy}{dx}\right)}^2+\sin (y)=0$.

Solution

1. The highest order derivative present in the equation is $\frac{d^{2}y}{d{x}^2}$, so the order is $2$.
2. The degree is the exponent of the highest order derivative when the equation is a polynomial in derivatives.
3. The exponent of $\frac{d^{2}y}{d{x}^2}$ is $3$.
4. Hence the answer is (A).