Question

Determine the order and degree of the given differential equation: $\sqrt{1+\frac{1}{(\frac{dy}{dx})^{2}}} = (\frac{d^{2}y}{dx^{2}})^{ \frac{3}{2}}$

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

$\sqrt{1+\frac{1}{(\frac{dy}{dx})^{2}}} = (\frac{d^{2}y}{dx^{2}})^{ \frac{3}{2}}$
taking square both sides

$1+\frac{1}{(\frac{dy}{dx})^{2}}= (\frac{d^{2}y}{dx^{2}})^{3}$
here we can see that highest order derivative is 2,

ie Order is 2.

and the complete equation is free from radicals now ,so here power of second order derivative is 3

So, Degree = 3