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Question

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=2cc=ydydx
Hence differential equation is
y2=2ydydx(x+ydydx)y2dydxx=ydydx
Squaring and multiplying by (dydx)2
y(dydx)3x2(dydx)2+xy(dydx)y24=0
Hence order is 1 and degree is 3.

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