Question

The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^3 + \left( \frac{dy}{dx} \right)^2 + \sin\left( \frac{dy}{dx} \right) + 1 = 0\], is

Options

• 3

• 2

• 1

• not defined

Answer 1

not defined

 

We have,

\[\left( \frac{d^2 y}{d x^2} \right)^3 + \left( \frac{dy}{dx} \right)^2 + \sin\left( \frac{dy}{dx} \right) + 1 = 0\]

\[\text{ The highest order derivative in this equation is }\frac{d^2 y}{d^2 x}.\]

But the equation cannot be expressed as a polynomial in differential coefficient.

Hence, the degree is not defined .