Find the sum of the order and the degree of the following differential equations:

Order of a differential equation is the order of the highest order derivative occurring in the differential equation

As, the given equation has highest order derivative of order 2, the order of given differential equation is 2.

Now, degree of a differential equation is defined if it is a polynomial equation of derivatives, the given equation is not a polynomial equation of derivatives because has a power and polynomial contains only integer powers.

Therefore, first we will convert the equation into polynomial of derivatives!

Cubing both sides, we get

Apply the formula (a + b)³ = a³+3a²b+3ab²+b³ in.

Since,

Degree of a differential equation is the highest power of the highest order derivative in it,

The highest power of highest order derivative is 3, therefore degree of given equation is 3.

Hence, order + degree = 2 + 3 = 5