The order and degree of the differential equation $\left( 1 + \left( \frac{dy}{dx} \right)^{2} \right)^{\frac{3}{4}} = \left( \frac{d^{2}y}{dx^{2}} \right)^{\frac{1}{3}}$is

Question

Dr. Abubacker · Accepted Answer

(a)
Given differential equation can be rewritten as
$\left\lbrack 1 + \left( \frac{dy}{dx} ight)^{2} ightbrack^{\frac{3}{4} 	imes 12} = \left( \frac{d^{2}y}{dx^{2}} ight)^{\frac{1}{3} 	imes 12}$
$\Rightarrow$ $\left\lbrack 1 + \left( \frac{dy}{dx} ight)^{2} ightbrack^{9} = \left( \frac{d^{2}y}{dx^{2}} ight)^{4}$
Here, we see that order of highest derivative is 2 and degree is 4.

Q. The order and degree of the differential equation $\left( 1 + \left( \frac{dy}{dx} \right)^{2} \right)^{\frac{3}{4}} = \left( \frac{d^{2}y}{dx^{2}} \right)^{\frac{1}{3}}$is

Explanation

Reviewed by Dr. Abubacker

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