Math Answers

Verify that the given differential equation is an exact: 

(3x²+2y)dx+(x-4y)dy=0

 Solve the first order linear inhomogeneous differential equation using the Bernoulli method

y^,-(2y/x)=1+(1/x)

Solve the first order linear inhomogeneous differential equation using the constant variation method

y^,- (3y/x)=x

Use the Principle of Mathematical Induction to prove that (2𝑛)! /(2ⁿ)𝑛! is odd for all positive integers.

Given the following 2 premises, 1. 𝑝 → (𝑞 ∨ 𝑟) 2. 𝑞 → 𝑠 Prove 𝑝 → (𝑟 ∨ 𝑠) is valid using the Proof by Contradiction method. 

Sam and Peter had $42 and $30 respectively. They each spent the same amount of money on a pair of shoes. How much was the pair of shoes if Sam had twice as much money as Peter after buying the pair of shoes?

F. How many different sequences, each of length r, can be formed using elements

from A if

(a) elements in the sequence may be repeated?

(b) all elements in the sequence must be distinct?

F. Find the integral surface of the linear partial differential equation x(x^2+z)p - y(y^2+z)q = (x^2-y^2)z; p, q has their usual meaning , which contains the straight line. [CO1] *

Show that the following logical equivalences hold for the

Peirce arrow ↓, where P ↓ Q ≡ ∼(P ∨ Q).

a. ∼P ≡ P ↓ P

b. P ∨ Q ≡ (P ↓ Q) ↓ (P ↓ Q)

c. P ∧ Q ≡ (P ↓ P) ↓ (Q ↓ Q)

H d. Write P → Q using Peirce arrows only.

e. Write P ↔ Q using Peirce arrows only.

F. Define and give examples of injective surjective and bijective functions. Check the injectivity and surjectivity of the following function f: NN given by f(x)=x2