Question

What is the degree of the following differential equation?

\(\rm x=\sqrt{1+\frac{d^2y}{dx^2}}\)

1. 1
2. 2
3. 3
4. Degree is not defined

Answer 1

Correct Answer - Option 1 : 1

Concept:

Order of a differential equation is the highest order of derivative that occurs in the differential equation.

Degree of a differential equation is the highest power of the highest order derivative that occurs in the equation, after all the derivatives are converted into rational and radical free form.

 

Calculation:

Getting rid of the radicals by raising both the sides to power 2 will give us:

\(\rm x^2=1+(\frac{d^2y}{dx^2})^1\)

The highest derivative in it is \(\rm \frac{d^2y}{dx^2}\), therefore its order is 2.

∴ The highest power of this derivative in the equation is 1, therefore its degree is 1.