`(d^2y)/(dx^2)+(dy/dx)+y=0`

The order of the differential equation 2x^2(d^2y)/(dx^2)-3(dy)/(dx)+y=0 is

If y= e^((k+1)x) is a solution of differential equation (d^2y)/(dx^2) -(4dy)/(dx) + 4y =0 , then k equals

Find the order and degree of 2x^2(d^2y)/dx^2-3(dy)/(dx)+y=0

Find the order and degree of (d^3y)/dx^3+2((d^2y)/dx^2)^2-(dy)/(dx)+y=0

Find the order and degree of (d^3y)/dx^3+3(d^2y)/dx^2+3(dy)/(dx)+y=0 and also state whether its linear or non-linear.

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

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

If y=3e^(2x)+2e^(3x) , prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0 .

If y=ae^(2x)+be^(-x), show that (d^(2)y)/(dx^(2))-(dy)/(dx)-2y=0