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Question

The differential equations satisfied by the system of parabolas y2=4a(x+a) is:

A
y(dydx)22x(dydx)y=0
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B
y(dydx)2+2x(dydx)y=0
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C
y(dydx)+2x(dydx)y=0
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D
y(dydx)22x(dydx)+y=0
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Solution

The correct option is B y(dydx)2+2x(dydx)y=0
y2=4a(x+a) (1)
2yy=4a
yy=2a
by(1)y2=2yy(x+yy2)
y2=2yyx+(yy)2
y(y)2+2xyy=0
(as y0)

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