Question: Let u1 and u2 ED solutions .... (1) where p, q and r are continuous functions on an interval I and also p(x) is never

Let u1 and u2 ED solutions

.... (1)

where p, q and r are continuous functions on an interval I and also p(x) is never zero.
Show that if W = W(u1, u2), then

....(2)

Then demonstrate that by making use of ED and the fact that u1 and u2 are solutions,
you get that

......(3)

Finally, resolve the previous ED 4. (10 puntos) Sean uz y uz soluciones de la ED p(x)u"

4. (10 puntos) Sean uz y uz soluciones de la ED p(x)u" + q(x)u' + r(x)u = 0 donde p, q yr son funciones continuas en un intervalo I y adems p(x) nunca es cero. Demuestre que si W = W (u1, u2), entonces dW -= u,p(x)u% uzp(x)u p(x) dx Luego demuestre que al hacer uso de la ED y el hecho de que u, y uz son soluciones, se obtiene que dw p(x) + q(x)W = 0 dx Por ltimo, resuelva la ED anterior.

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