Question

Why is the degree of the differential equation \[y'' + \sin(y') = 0\] not defined?

Options

• Because the equation is not linear

• Because the equation contains a second-order derivative

• Because the equation does not have a first-order derivative

• Because the derivative appears in a non-polynomial form (inside a sine function)

Answer 1

Degree is defined only for polynomial equations in derivatives. Since the term \[\sin(y')\] contains the derivative in a trigonometric (non-polynomial) form, the equation is not polynomial in its derivatives. Therefore, the degree is not defined for this equation.