Show that `y=A x+B/x ,x!=0` is a solution of the differential equation `x^2(d^2y)/(dx^2)+x(dy)/(dx)-y=0`

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

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

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

Show that y=b e^x+c e^(2x)\ is a solution of the differential equation (d^2y)/(dx^2)-3(dy)/(dx)+2y=0.

Show that y=be^(x)+ce^(2x) is a solution of the differential equation (d^(2)y)/(dx^(2))-3(dy)/(dx)+2y=0

Show that y=be^(x)+ce^(2x) is a solution of the differential equation (d^(2)y)/(dx^(2))-3(dy)/(dx)+2y=0

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

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