Find the order and degree of the differential equation $\frac{d^{2}y}{d{x}^2}=(1+(\frac{dy}{dx}{)}^2{)}^{3/2}$.

Solution

1. The given differential equation is $\frac{d^{2}y}{d{x}^2}=(1+(\frac{dy}{dx}{)}^2{)}^{3/2}$.
2. The highest order derivative present is $\frac{d^{2}y}{d{x}^2}$, so the order of the differential equation is 2.
3. To find the degree, square both sides to remove the fractional exponent: $(\frac{d^{2}y}{d{x}^2}{)}^2=(1+(\frac{dy}{dx}{)}^2{)}^3$.
4. Since the highest power of the highest order derivative is 2, the degree of the differential equation is 2.
5. Hence the answer is (B).