need help please for 32 32. Let yı and y2 be two solutions of A(x)y" + B(x)y' +C(x)yare continuous and A(x) is never zero. (a) Let W =W(y1, y2). Show that= 0 on an open interval I where A, B, and CdWA(x)-dx= (v1)(Ay") – (y2)(Ay{).Then substitute for Ay and Ay from the original differ-ential equation to show thatdWA(x)3 — В (х) W(x).dx(b) Solve this first-order equation to deduce Abel's for-mulaB(x)W(x) = K exp (- /AG dx).where K is a constant. (c) Why does Abel's formulaimply that the Wronskian W(y1, y2) is either zero every-where or nonzero everywhere (as stated in Theorem 3)?Apply Theorems 5 and 6 to find general solutions of the dif-ferential equations given in Problems 33 through 42. Primesdenote derivatives with respect to x.

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Description: need help please for 32 32. Let yı and y2 be two solutions of A(x)y" + B(x)y' +C(x)yare continuous and A(x) is never zero. (a) Let W =W(y1, y2). Show that= 0 on an open interval I where A, B, and CdWA(x)-dx= (v1)(Ay") – (y2)(Ay{).Then substitute for

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Answered: 32. Let yı and y2 be two solutions of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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need help please for 32

32. Let yı and y2 be two solutions of A(x)y" + B(x)y' +
C(x)y
are continuous and A(x) is never zero. (a) Let W =
W(y1, y2). Show that
= 0 on an open interval I where A, B, and C
dW
A(x)-
dx
= (v1)(Ay") – (y2)(Ay{).
Then substitute for Ay and Ay from the original differ-
ential equation to show that
dW
A(x)
3 — В (х) W(x).
dx
(b) Solve this first-order equation to deduce Abel's for-
mula
B(x)
W(x) = K exp (- /
AG dx).
where K is a constant. (c) Why does Abel's formula
imply that the Wronskian W(y1, y2) is either zero every-
where or nonzero everywhere (as stated in Theorem 3)?
Apply Theorems 5 and 6 to find general solutions of the dif-
ferential equations given in Problems 33 through 42. Primes
denote derivatives with respect to x.

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