QJEEM21Ma85c8: JEE Main 2021 Mathematics - Class 12 JEEM21Ma85c8 Solution: The difference between degree and order of a differential…

Question

Verified Solution • 2025–26 Session moderate

The difference between degree and order of a differential equation that represents the family of curves given by

{y^2} = a\left( {x + {{\sqrt a } \over 2}} \right)

, a > 0 is _________.

Accepted Answer

{y^2} = a\left( {x + {{\sqrt a } \over 2}} \right)

Differentiating both sides, we get

2yy' = a

{y^2} = 2yy'\left( {x + {{\sqrt {2yy'} } \over 2}} \right)

y = 2y'\left( {x + {{\sqrt {yy'} } \over {\sqrt 2 }}} \right)

y - 2xy' = \sqrt 2 y'\sqrt {yy'}

{\left( {y - 2x{{dy} \over {dx}}} \right)^2} = 2y{\left( {{{dy} \over {dx}}} \right)^3}

D = 3 & O = 1

\therefore

D

-

O = 3

-

1 = 2

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