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Order=2, Degree-Not defined , Non- linear

Hint:

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.

Given:

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

Solution:

Concept of the question

For the degree to be defined of any differential equation, the equation must be expressible in the form of a polynomial.

But in this question the degree of the differential equation is not defined because the term on the right hand side is not expressible in the term of a polynomial.

Here in this question, the order of the differential equation is 2 and the degree of the differential equation is not defined.

Since the degree of the equation is not defined, the equation is non-linear.

Therefore, Order=2, Degree=Not defined, Non- linear

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