Determine the order and degree of the differential equation:
$open square brackets 1 plus open parentheses dy over dx close parentheses squared close square brackets to the power of 3 over 2 end exponent space equals 5 fraction numerator straight d squared straight y over denominator dx squared end fraction$

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Solution

The given differential equation is

open square brackets 1 plus open parentheses dy over dx close parentheses squared close square brackets to the power of 3 over 2 end exponent space equals space 5 fraction numerator straight d squared straight y over denominator dx squared end fraction

This can be written as

open square brackets 1 plus open parentheses dy over dx close parentheses squared close square brackets to the power of 3 over 2 end exponent space equals space 25 open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses squared

∴ degree of differential equation is 2 and order 2.

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