The degree of the differential equation

Question:

The degree of the differential equation

$\left(\frac{d^{2} y}{d x^{2}}\right)^{2}+\left(\frac{d y}{d x}\right)^{2}=x \sin \left(\frac{d y}{d x}\right)$ is:

(A) 1

(B) 2

(C) 3

(D) not defined

Solution:

Correct option is (D) not defined.

Since the value of sin (dy/dx) on expansion will be in increasing power of dy/dx, the degree of the given differential equation is not defined.

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