Question

The degree of the differential equation `1 + (dy/dx)^2 = x` is ______.

Answer 1

The degree of the differential equation `1 + (dy/dx)^2 = x` is 2.

Explanation:

Given differential equation:

`1 + (dy/dx)^2 = x`

Step 1: Definition of Degree 

The degree of a differential equation is the power of the highest order derivative after the equation is made free from radicals and fractions involving derivatives.

Step 2: Identify the highest order derivative 

Here, the highest order derivative is:

`dy/dx`

It apperrs as:

`(dy/dx)^2`

Step 3: Degree

The highest power of the highest order derivative is 2.