Question

The degree of the equation ${\left(\frac{d^{2}y}{d{x}^2}\right)}^3-4⁤\frac{dy}{dx}=2$ is

1. 0
2. 1
3. 2
4. 3

Answer: 3

Solution :-

The highest order derivative present in the given differential equation is $\frac{d^{2}y}{d{x}^2}$ and this is 2nd order derivative, so its order is one. It is a polynomial equation in $\frac{d^{2}y}{d{x}^2}$ and $\frac{dy}{dx}$ and the highest power raised to highest order derivative $\frac{d^{2}y}{d{x}^2}$ is three, so its degree is three.

So, correct answer is option-4, $\to 3$