1 Differential Equations
The differential equation for the family of curves x2 + y2-2ay =0, where a is an arbitrary constant is
1) 2(x2-y2)y'=xy 2) 2(x2 + y2)y'=xy 3) (x2-y2)y'= 2xy 4) (x2 + y2)y'=2xy
SOLUTION
2x + 2yy′ - 2ay′ = 0
(eliminating a)
⇒ (x2 – y2 )y′ = 2xy.
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