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## Main Question or Discussion Point

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

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