The differential equations satisfied by the system of parabolas y2=4ax+a is:
ydydx+2xdydx-y=0
ydydx2+2xdydx-y=0
ydydx-2xdydx-y=0
ydydx-2xdydx+y=0
Explanation for correct option
Finding the differential equation
Given equation, y2=4a(x+a).......1On differentiating w.r.t.x:2ydydx=4a⇒a=y2dydxOn substituting a in equation 1:y2=4yzdydx(x+a)⇒y=2dydx(x+a)⇒y=dydxx+y2dydx⇒y=2xdydx+y2dydx2∴ydydx2+2xdydx-y=0Hence, the correct answer is Option (B).