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

Verify that the function y=e^(-3x) is a solution of the differential equation (d^2y)/(dx^2)+(dy)/(dx)-6y=0

Verify that the function y=e^(-3x) is a solution of the differential equation (d^2y)/(dx^2)+(dy)/(dx)-6y=0

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

Verify that y=4sin3x is a solution of the differential equation (d^2y)/(dx^2)+9y=0.

Verify that y=4sin3x is a solution of the differential equation (d^2y)/(dx^2)+9y=0.

Verify that y=c e^(t a n-1_x) is a solution of differential equation (1+x^2)(d^2y)/(dx^2)+(2x-1)(dy)/(dx)=0.

Solution of the differential equation x((dy)/(dx))^(2)+2sqrt(xy)(dy)/(dx)+y=0 is

The solution of differential equation (d^2y)/(dx^2)=dy/dx,y(0)=3 and y'(0)=2 :