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# Partial Differential Equations

### Differential Equation: Partial Integrals

For this problem state the menthod you used and show the work required to obtain the answer. Find the complete solution to each of the equation problem: 4y^2 - 4y^1 + y = e^(x/2) * square root of (1-x^2)

### Proving a partial order and total order.

Say whether or not R is a partial order and a total order on A. Show proof. A= {a,b,c}, R= {(a,a),(b,a),(b,b),(b,c),(c,c)

### Partial order and total order

In each of the following say whether or not R is a partial order on A. If so, is it a total order? a) A= {a,b,c,d}, R= {(a,a),(b,a),(b,b),(b,c),(c,c)} b) A is the set of positive divisors of 24, that is A= {1,2,3,4,6,8,12,24}, and the relation R is dividing. If B is the set of positive divisors of 24 except 1, what is the

### Reflexive, symmetric, antisymmetric, transitive, partial order

Let R = {(1,1)(3,1)(2,2)(1,2)(3,3)(3,2)} on Z = {1,2,3} Is R reflexive? Why? Is R Symmetric? Why? Is R antisymmetric? Why? Is R transitive? Why? Is R a partial order? Why? Is R an equivalence relation?

### Antisymmetric, transitive, and partial order relations

Let R be a relation on all real numbers x, y such that x is related to y if and only if x^2 <= y^2. Is R antisymmetric? transitive? a partial order relation? Prove or give a counter example.