Differential Equations Answers

Solve the equation x^2×d^2y/dx^2+x×dy/dx +y = x^m , for all positive integer values of m.

Given that y1(x)= x^-1is one solution of the differential equation 2x^2y"+3xy'-y=0,x>0, find a second linearly independent solution of the equation.

Write the ordinary differential equation ydx+(xy+x-3y)dy=0 in the linear form , and hence find its solution.

Solve dy/DX +xy= y^2e^x^2/2sin x

The pde uxx+ x^2 uxy -(x^2/2+1/4) uyy = 0 is hyperbolic in the entire xy-plane.true or false why?

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.