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JEE Main202126 Feb 2021Morning ShiftMathematicsDifferential EquationsActual

The difference between degree and order of a differential equation that represents the family of curves given by y 2 = a x + a 2 , a > 0 is _______.

Correct answer

0

Step-by-step solution

y 2 = a x + a 2 = a x + a 3 / 2 2 . . . 1 ⇒ 2 y y ' = a Put in equation 1 we get, y 2 = 2 y y ' x + 2 y y ' 3 / 2 2 y 2 - 2 x y y ' = 2 y y ' 3 / 2 2 Squaring both the sides we get, y 2 - 2 x y y ' 2 = 2 y 3 y ' 3 ∴ Order = 1 Degree = 3 Degree - order = 3 - 1 = 2

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