Find the equation of the curve passing through the origin if the middle point of the segment of its normal from any point of the curve to the x-axis lies on the parabola 2y2=x
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If xdy=ydx+y2dy,y>0 andy(1)=1, then what is y(−3) equal to?
The solution of the differential equationxsinxdydx+(xcosx+sinx)y=sinx. When y(0)=0 is
The solutions of (x+y+1) dy=dx are
The solution of the differential equation 2x2ydxdy=tan(x2y2)−2xy2, given y(1)=2π, is
The normal to a curve at P(x,y)
meet the x-axis at G˙
If the distance of G
from the origin is twice the abscissa of P
, then the curve is a
(a) parabola (b) circle
(c) hyperbola (d) ellipse