Question

For the differential equation \[y''' + y^{2} + e^{y'} = 0\], is the degree defined?

Options

• Degree is not defined

• Degree = 3

• Degree = 1

• Degree = 2

Answer 1

The degree exists only for equations that are polynomial in their derivatives. In this equation, the term \[e^{y'}\] contains the derivative \[y'\] as an exponent in an exponential function, making it non-polynomial in its derivatives. Therefore, the degree is not defined.