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

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+Bsinx) is the solution of the differential equation (d^2y)/(dx^2)-2(dy)/(dx)+2y=0.

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

Show that y=a cos(log x)+b sin(log x) is a solution of the differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0