Question

Find the order and degree of the following differential equations :

(i) a(d²y/dx²) = [1 + (dy/dx)²]^3/2

(ii) xdx + ydy = 0

Answer 1

(i) a(d²y/dx²) = [1 + (dy/dx)²]^3/2

The highest derivative of y = (d²y/dx²)²

Thus, order = 1, degree = 4.

(ii) xdx + ydy = 0

⇒ x + ydy/dx = 0

The highest derivative of y = dy/d1x = (d¹y/dx¹)¹

Thus, order = 1, degree = 1.