selecting independent variables from the general solution
I have got a general solution for the equation
xy'' - y' + 4x^3y = 0, x > 0
by converting to the normal version of the self adjoint form and solving with an auxiliary equation I have
y = Acos(2x) + Bsin(2x)
It then asks to select two independent solutions and verify the wronskian satisfies Abel's identity.
Can I simply set A = 0, B = 1 for y1 and A = 1, B = 0 for y2
I did this and I got 1 for the wronskian and kx for Abel's which doesn't prove it!!!
Can anybody tell me where I'm going wrong please