Question

Answer the following question in one word or one sentence or as per exact requirement of the question.
Write the degree of the differential equation ${\left(\frac{dy}{dx}\right)}^4+3x\frac{d^{2}y}{d{x}^2}=0$.

Answer 1

The differential equation must be a polynomial equation in derivatives for the degree to be defined.

The degree of the differential equation is represented by the power of the highest order derivative in the given differential equation.

${\left(\frac{dy}{dx}\right)}^4+3x\frac{d^{2}y}{d{x}^2}=0$ is a polynomial equation in derivatives.

Here the highest order is 2.

and the power of the highest order derivative is 1.

So, the degree of the given differential equation is $1$.