Question

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

(d³y)/(dx² ))^1/2 = (1 + (dy)/(dx))²

\((\frac{d^3y}{dx^3})^{1/2}=(1+\frac{dy}{dx})^2\)

Answer 1

Given differential equation is

\((\frac{d^3y}{dx^3})^{1/2}=(1+\frac{dy}{dx})^2\) 

By squaring both sides, we get

\(\frac{d^3y}{dx^3}=(1+\frac{dy}{dx})^4\) 

⇒ \(\frac{d^3y}{dx^3}-(\frac{dy}{dx})^4-4(\frac{dy}{dx})^3-12(\frac{dy}{dx})^2-4 - \frac{dy}{dx}-1 = 0\)

which is a differential equation of order 3 and degree 1.

\(\therefore\) Sum of order and degree  = 3 + 1 = 4