Question

Find the order and degree of the following differential equations :

(i) (d²y/dx²)³ + y(dy/dx)² + y⁵ = 0

(ii) x(dy/dx) + 3/(dy/dx) = y²

Answer 1

(i) (d²y/dx²)³ + y(dy/dx)² + y⁵ = 0

The highest derivative of y = (d²y/dx²)³

Thus, order = 2, degree = 3.

(ii) x(dy/dx) + 3/(dy/dx) = y²

x(dy/dx)² + 3 = y²(dy/dx)

The highest derivative of y = (dy/dx)² = (d¹y/dx¹)²

Thus, order = 1 degree = 2.