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This is the question that was asked:

Does the Wronskian of solutions of a linear homogeneous DE evolve in $t$ in any reasonable way? ($t$ being a variable.) What can you say about the Wronskian without actually solving the equation?

So I know that the Wronskian can show if a set of solutions is linearly independent if it is nonzero. On the other hand it shows linear dependency when it is zero. Also, if the Wronskian is nonzero, then the solutions form a fundamental set of solutions for the said DE. This being said, I think that answers the second question above. However, I am very lost with how it "evolve[s] in $t$", could this be explained?

Thanks!

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Wronskian will evolve with time depending only on the first and second term of the ODE. This is called Abel's identity. You may find it on wiki.

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  • $\begingroup$ This does not comprehensively answer the question $\endgroup$
    – Shailesh
    Mar 12 '16 at 5:50
  • $\begingroup$ @Rui, after looking up Abel's identity I came across the fact that the Wronskian(y1,y2)(x)= W(y1,y2)(x0)exp(-(integral from x0 to x of [p(s)ds]. So would it be dependent only on p(x)? Where p(x) is the coefficient of y'. $\endgroup$
    – Lauren
    Mar 13 '16 at 4:46

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