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

Verify that y=a/x+b is a solution of the differential equation (d^(2)y)/(dx^(2))+2/x((dy)/(dx))=0.

Verity that y=a/x+b is a solution of the differential equation (d^2y)/(dx^2)+2/x((dy)/(dx))=0.

Show that the function y=Ax+B/x is a solution of the differential equation x^2(d^2y)/dx^2+xdy/dx-y=0 .

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

Verify that the function y=a cos x + b sin x is a solution of the differential equation cos x(dy)/(dx)+y sin x =b

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

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

A solution of the differential equation y'=y is

Show that \ y=A e^(B x) is as solution of the differential equation (d^2y)/(dx^2)=1/y((dy)/(dx))^2dot