Problem 4.14. Suppose that a, b e Z, and that a, b + 0. Show that f(r, y) = ax + by is a Latin square.

7.The Legendre equation of order α is (1−x2)y′′−2xy′+α(α+1)y=0.1−x2y″−2xy′+αα+1y=0. The solution of this equation near the ordinary point x = 0 was discussed in Problems 17 and 18 of Section 5.3. In Example 4 of Section 5.4, it was shown that x = ± 1 are regular singular points. a.Determine the indicial equation and its roots for the point x = 1. b.Find a series solution in powers of x − 1 for x − 1 > 0. Hint: Write 1 + x = 2 + (x − 1) and x = 1 + (x − 1).Alternatively, make the change of variable x − 1 = t and determine a series solution in powers of t.

1) Find the general solution of the equation x³y" - 2x²y" - 4xy' + 8y = x² + Inx.

ASAP

A Moving to another question will save this response. Question 11 Find the general solution of Xy" + xy -4y 0 where y(1) =0 and y (1) = 4

Can someone help me answer these problems .1 and 3 .please

Question 4 please sectio. 8.5

1. What is the answer? Use a given-required-solution format without using a calculator. Provide a step-by-step solution and simplify your answer. Use a handwritten calculation.

7. Show that I (A)(3)(2)("-") = 1 (2π)(m-1)/2 m