Question

16. The general solution of the differential equation x dy-0 is(A)xy=C(B) x=Of(C) y=Cr(D) y=Cr2

Answer 1

sThe given differential equation is,

ydx−xdy y =0

The above equation can be written as,

ydx y − xdy y =0 dx x = dy y

Integrate both sides of above differential equation,

∫ dx x = ∫ dy y logx=logy+log C 1 logx−logy=log C 1 log x y =log C 1

Further, simplify the differential equation.

x y = C 1 y= x C 1 y=Cx                    [ 1 C 1 =C ]

Hence, the correct option is (C).