Verify that `y=e^x(acosx+csinx)` is a solution of the differential equation `(d^2y)/dx^2-2(dy)/(dx)+2y=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.

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

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=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

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

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

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

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

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