2(d^2 y/dx^2) + 3√1-(dy/dx)^2 - y = 0

Question

Determine the order and degree of each of the following differential equations. State also whether they are linear or non-linear.

\(2\frac{d^2y}{dx^2} + \sqrt [3]{1-\left(\frac{dy}{dx} \right)^2}-y=0\)

Answer 1

The order is the highest numbered derivative in the equation with no negative or fractional power of the dependent variable and its derivatives, while the degree is the highest power to which a derivative is raised.

The above equation can be written as

Since the equation has rational powers, we need to remove them so squaring both sides we get

So, the order of the above differential equation 2 and the degree of the differential equation is 2.

In a differential equation, when the dependent variable and their derivatives are only multiplied by constants or independent variable, then the equation is linear.

So, in this question, the dependent variable is y and the term \(\frac{dy}{dx}\) is multiplied by itself, so the given equation is non-linear.