This is the reference book, please answer the following question. Ravi P. Agarwal Donal O'Regan An Introduction to Ordinary Differential Equations Please answer Question 1 from chapter 4 of above mentioned book, all references are attached. Lecture 4 Elementary First-Order Equations Suppose in the DE of first order (3.1). M(r,y) = X₁(r), (y) and N()-X2()(), so that it takes the form X()() | X()2(n) = 0. (4.1) If Y₁(y)X(r) 0 for all (r,y) e S, then (4.1) can be written as an exact DE X₁(z) Y₂(v) X2()() + = 0 (4.2) in which the variables are separated. Such a DE (4.2) is said to be separable. The solution of this exact equation is given by -de + Y₁(w) (1.3) Here both the integrals are indefinite and constants of integration have been absorbed in c. Equation (4.3) contains all the solutions of (4.1) for which Yi (2) X₂() 0. In fact, when we divide (1.1) by YX2 we might have lost some solutions, and the ones which are not in (4.3) for some e must be coupled with (4.3) to obtain all solutions of (4.1). Example 4.1. The DE in Example 3.2 may be written as 1 1 = 0, ry(1-3) 0 y(1-y) for which (4.3) gives the solution y = (1-er)-1. Other possible solutions for which (-2)=0 are r = 0, y = 0, and y = 1. However, the solution y = 1 is already included in y= (1-cr) for c=0, and r=0 is not a solution, and hence all solutions of this DE are given by y = 0, y = (1-cr). A function f(x, y) defined in a domain D (an open connected set in IR²) is said to be homogeneous of degree k if for all real A and (x, y) = D f(x,y) = *(3) (4.4) For example, the functions 32-ry-y², sin(x²/(x²- y²)), (x² + 7y)1/5, (1/2) sin(x/y)+(x/y3)(Iny-Inz), and (6e//r2/31/3) are ho- mogeneous of degree 2, 0, 4/5, -2, and -1, respectively. In (4.4) if A 1/2, then it is the same as f(x,y). (4.5) This implies that a homogeneous function of degree zero is a function of a single variable v (=y/x).

Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

/www.mathxl.com/Student/PlayerHomework.aspx?homeworkld=611416809&questionld=1&flushed%3false&cld%3D6709552¢erwin-yes MAT 234-KA: Elementary Differential Equations junior E Homework: Section 7.4 HW Score Question 4, 7.4.26 > points O Points Determine L{F}. 8s - 14s- Ss+7 F(s) = s (s - 7) %D Clear all View an example Get more help - Help me solve this

Please draw and make a short explanation about of this pmf : p(y) = 1/(y+1) for y = 0, 1, ..., 6.