d^4y/dx^4 + sin (dy/dx) = 0

Question

Determine the order and degree of the following differential equation:

\(\cfrac{d^4y}{dx^4}+sin(\frac{dy}{dx})=0\)
d⁴y/dx⁴ + sin (dy/dx) = 0

Answer 1

The given D.E. is \(\cfrac{d^4y}{dx^4}+sin(\frac{dy}{dx})=0\)
This D.E. has highest order derivative \(\cfrac{d^4y}{dx^2}\) . 

∴ order = 4

Since this D.E. cannot be expressed as a polynomial in differential coefficient, the degree is not defined.