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.

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

Verify tht y=e^(x) cos bx is a solution of the differential equation (d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0.

y = log x + c is a solution of the differential equation x(d^(2)y)/(dx^(2)) + (dy)/(dx) = 0

Verify that y=-x-1 is a solution of the differential equation (y-x)dy-(y^(2)-x^(2))dx=0

Verify that y=cx+2c^(2) is a solution of the differential equation 2((dy)/(dx))^(2)+x(dy)/(dx)-y=0

Show that y=ae^(2x)+be^(-x) is a solution of the differential equation (d^(2)y)/(dx^(2))-((dy)/(dx))-2y=0