y=logx+c is a solution of the differential equation

Show that y=acos(logx)+bsin(logx) is a solution of the differential equation x^2(d^2y)/(dx^2)+(dy)/(dx)+y=0.

A solution of the differential equation y'=y is

Show that y=c x+a/c is a solution of the differential equation y=x(dy)/(dx)+a/((dy)/(dx))dot

y=x^(m) is a solution of the differential equation

y=a+b/x is a solution of the differential equation

y=a+b/x is a solution of the differential equation

y=a+b/x is a solution of the differential equation

y secx=tan x+c is a solution of the differential equation

y=(sin^(-1)x)^(2)+c is a solution of the differential equation

y = sin 3x is a solution of the differential equation