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+ 2xy = f(x), y(0) = 2, and y(x) be continous everywhere dx where f(x) = = (x, if 0 ≤ x < 1 10, if x ≥ 1

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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Question

Find the general solution (and a particular solution for the IVP) and determine whether there is any transient
term in the general solution

3
+ 2xy = f(x), y(0) =, and y(x) be continous everywhere
dx
where f(x)= =
(x, if 0 ≤ x < 1
10,
if x ≥ 1

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Let A and B represent two variants (alleles) of the DNA at a certain locus on the genome. Assume that 40% of all the alleles in a certain population are type A and 30% are type B. The locus is said to be in Hardy- Weinberg equilibrium if the proportion of organisms that are of type AB is (0.40) (0.30) = 0.12. In a sample of 300 organisms, 42 are of type AB. Can you conclude that this locus is not in Hardy-Weinberg equilibrium?
Create a 2nd order, homogeneous, linear IVP, that is not guaranteed to have a unique solution at x_0=3. Be sure to state why your IVP works and be sure to comment on a classmates post.