Question

Determine the order and degree of the given differential equation: $(\frac{d^{2}y}{dx^{2}})^{2}+\cos (\frac{dy}{dx})=0$

Answer 1

Solution:
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➡️Order of a DE: Order is calculated by checking higher order derivative of x. All DE have order.

➡️Degree of DE: Degree is the power of highest order derivative,when complete equation is free from radicals. Every differential equation does not have degree.

Here in the give DE

$(\frac{d^{2}y}{dx^{2}})^{2}+\cos (\frac{dy}{dx})=0$

here highest derivative is :2
As we know that $\frac{d^{2}y}{dx^{2}}$

ie Order is 2.

and the complete equation is free from radicals, but first derivative comes with cos (dy/dx), thus the given differential equation is not applicable to calculate degree .

So, Degree = None.