Differential Equations Answers

The solution of the pde dz/dx +dz/dy = z^2 is z = -[y+f(x-y)] true or false why?

The initial value problem dy/dx = x^2+y^2, y(0) = 0 has a unique solution in some interval of the form -h<x<h. True or false ,why?

solve; [D^3 − DD′^2 − D^2 + DD′] z = 0

Q1.A Company uses 2,500 units during the course of the year, and its usage is relatively constant throughout the year. These units are purchased from a supplier 100 kilometers away for Ksh.15 each, and the lead time is 2 days. The holding cost per unit per year is Ksh.1.50 (or 10% of unit cost) and the ordering cost per order is Ksh.18.75. There are 250 working days per year for this company.
a) What is EOQ?
b) Given the EOQ, what is the average inventory?
c) In minimizing cost, how many orders would be made each year? What would be the annual ordering cost?
d) Given the EOQ, what is the total annual inventory cost ( including purchase cost)
e) What is the time between orders?
f) What is the ROP(re-oder point)? (15mks)

Write a linear first-order differential equation and work out its general solution.

Calculate the surface integral, F.ds, where F = 2(x,y,z), and where S is the surface of the cube define by the relations 0≤x≤1, 0≤y≤1, 0≤z≤1.

Q. Find the ordinary point and the singular point of the differential equation
(1+x2)y’’+xy’-xy=0

Q. Find the ordinary point and the singular point of the differential equation
Y’’-xy’+2y=0