Write the sum of the order and degree of the differential equation (d^2y/dx^2 + (dy/dx + x^4 = 0))

Question

Write the sum of the order and degree of the differential equation

\((\frac{d^2y}{dx^2})^2 + (\frac{dy}{dx})^3 + x^4 = 0\)

Answer 1

Given, differential equation is

 \((\frac{d^2y}{dx^2})^2 + (\frac{dy}{dx})^3 + x^4 = 0\)

Here, we see that the highest order derivative is \(\frac{d^2y}{dx^2}\), whose degree is 2.

Here, order = 2 and degree = 2

Thus, sum of the order and degree = 2 + 2 = 4