Question

The degree of the differential equation

\(\dfrac{d^2y}{dx^2}+3\left(\dfrac{dy}{dx}\right)^2 =x^2 \log \left(\dfrac{d^2y}{dx^2}\right)\)

1. 1
2. 2
3. 3
4. Not defined

Answer 1

Correct Answer - Option 4 : Not defined

Concept:

Order: The order of a differential equation is the order of the highest derivative appearing in it.

Degree: The degree of a differential equation is the power of the highest derivative occurring in it, after the Equation has been expressed in a form free from radicals as far as the derivatives are concerned.

Calculation:

\(\dfrac{d^2y}{dx^2}+3\left(\dfrac{dy}{dx}\right)^2 =x^2 \log \left(\dfrac{d^2y}{dx^2}\right)\)

For the given differential equation the highest order derivative is 2.

The given differential equation is not a polynomial equation because it involved a logarithmic term in its derivatives hence its degree is not defined.