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Use Abel's Theorem to approximate the Wronskian: $$y"-y'-12y=0; y_1=e^{-3x}, y_2=e^{4x}$$
I don't understand how to apply Abel's Theorem by referencing my textbooks explanation $W(y_1, y_2)(x)=(c)\text{exp}\left[-\int{p(x)dx}\right]$.
If someone could help me out that would be great!

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1 Answer

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Hint:

If $y_1$ and $y_2$ are solutions to the DEQ, $y'' + p(x) y' + q(x) y = 0$, then the Wronskian is given by:

$$W = ce^{-\int p(x)~dx}$$

For your DEQ, we have:

$$p(x) = -1$$

Spoiler

$W(y_1,y_2) = ce^x$ (Note: this gives us the Wronskian up to a multiplicative constant (the actual Wronskian is $W(y_1,y_2) = 7e^x)$.

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