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

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

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

The solution of the differential equation (d^(2)y)/(dx^(2))=e^(-2x) , is

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

Show that y=e^(2x) is a solution of differential equation (d^(2)y)/(dx^(2))+(dy)/(dx)-6y=0

Show that y=e^(x)(A cos x+B sin x) is the solution of the differential equation (d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0

Show that y=x sin x is a solution of the differential equation (d^(2)y)/(Dx^(2))+y-2cosx=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.