The order and degree of the differential equation [ 4 + ( d y d x ) 2 ] 2 / 3 = d 2 y d x 2 are Options: A . &nbsp 2,2 B . &nbsp 3,3 C . &nbsp 2,3 D . &nbsp 3,2

The order and degree of the differential equation [4+(dydx)2]2/3=d2ydx2 a

Discussion Forum : Differential Equations

Question -

The order and degree of the differential equation ${[4 + {(\frac{d y}{d x})}^{2}]}^{2 / 3} = \frac{d^{2} y}{d x^{2}}$ are

Options:

A . 2,2

B . 3,3

C . 2,3

D . 3,2

Answer: Option C
:
C

Here power on the differential coefficient is fractional, therefore change it into positive integer, so
${[4 + {(\frac{d y}{d x})}^{2}]}^{2 / 3} = \frac{d^{2} y}{d x^{2}} \Rightarrow {[4 + {(\frac{d y}{d x})}^{2}]}^{2} = {[\frac{d^{2} y}{d x^{2}}]}^{3}$
Hence order is 2 and degree is 3.

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