The differential equation representing the family of curves y2=2c(x+√c) where c is a positive parameter, is of
A
Order 1
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B
Order 2
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C
Degree 3
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D
Degree 4
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Solution
The correct options are A Order 1 C Degree 3 Given curve is y2=2c(x+√c). Differentiate w.r.t. x, 2ydydx=2c⇒c=ydydx Hence differential equation is y2=2ydydx(x+√ydydx)⇒y2dydx−x=√ydydx Squaring and multiplying by (dydx)2 y(dydx)3−x2(dydx)2+xy(dydx)−y24=0 Hence order is 1 and degree is 3.