The differential equation of the family of parabolas with focus at the origin and the x-axis as axis is
y(dydx)2+2 xy dydx+y=0
Equation of family of parabolas with focus at (0,0) and x - axis as axis is y2=4a(x+a)......(i) Differentiating (i) with respect to x, 2yy1=4a;y2=2yy1(x+yy12)y=2xy1+yy21⇒y(dydx)2+2xdydx=y.
The differential equation of family of curves y2=4a(x+a) is a) y2=4dydx(x+dydx) b) 2ydydx=4a c) yd2ydx2+(dydx)2=0 d) 2xdydx+y(dydx)2−y=0
Formation of the differential equation corresponding to the ellipse major axis 2a and minor axis 2b is:
The differential equation of the family of curves y2=4a(x+a), where a is an arbitrary constant, is