Question

Find the order and degree of the differential equation

`sqrt(1 + 1/(dy/dx)^2) = ((d^2y)/(dx^2))^(3/2)`

Answer 1

Given `sqrt(1 + 1/(dy/dx)^2) = ((d^2y)/(dx^2))^(3/2)`

Squaring both sides

`1 + 1/(dy/dx)^2 = ((d^2y)/(dx^2))^3`

∴ `(dy/dx)^2 + 1 = ((d^2y)/(dx^2))^3(dy/dx)^2`

∴ Degree = 3,

Order = 2