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The differential equation of the family of curves, x^2 = 4b(y + b), b ∈ R, is (1) x(y')^2 = x + 2yy'

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The differential equation of the family of curves, x2 = 4b(y + b), b ∈ R, is 

(1) x(y')2 = x + 2yy' 

(2) x(y')2 = 2yy' – x 

(3) xy" = y' 

(4) x(y')2 = x – 2yy'

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Answer is (1) x(y')2 = x + 2yy'

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Answer is (1) x(y')2 = x + 2yy'

2x = 4by ⇒ y' = 2x/4b

Required D.E. is x2 = 2x/y' y + (x/y')2

X(y')2 = 2yy' + x

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