Determine the reasonable form of the particular solution for each non homogeneous differential equation. Do not solve it.
a) y''y'2y= e^x+xcos2x+e^xsin2x.
b) D^2[y] +4y =1+x^2+xsin2x.
In: Advanced Math
Let a and b be integers and consider (a) and (b) the ideals they generate. Describe the intersection of (a) and (b), the product of (a) and (b), the sum of (a) and (b) and the Ideal quotient (aZ:bZ).
In: Advanced Math
1. Prove the HeineBorel Theorem (Theorem 3.35).
2. Suppose f: X → Y maps from the metric space X to the metric
space Y, and x ∈ X.
Prove that f is continuous at x if and only if, for any sequence
{xn} in X that converges to x, f(xn) → f(x).
In: Advanced Math
Solve SVM for a data set with 3 data instances in 2 dimensions: (1,1,+), (1,1,),(0,1,). Here the first 2 number are the 2dimension coordinates. ‘ +’ in 3rd place is positive class. And ‘‘ in 3rd place is negative class . Your task is to compute alpha’s, w, b. Then, Solve SVM when data are nonseparable, using k=2 when minimizing the violations of the misclassification, i.e., on those slack variables.
In: Advanced Math
For p = 5 , find a number x such that x^2 is congurent to 1 mod p. here x is denoted by sqrt(1). Determine if sqrt(1) exists mod p for p = 7, 11, 13 , 17, 23, 29.
In: Advanced Math
How many ways are there to choose three different numbers each
between one and a
hundred so that their sum is even? Explain
In: Advanced Math
Prove the following:
Let V and W be vector spaces of equal (finite) dimension, and let T: V → W be linear. Then the following are equivalent.
(a) T is onetoone.
(b) T is onto.
(c) Rank(T) = dim(V).
In: Advanced Math
2.31. Show that for each of the following values of a and b, there exists x, y in Z satisfying ax + by = 11. (i) a = 11, b = 0, (ii) a = 22, b = 11, (iii) a = 33, b = 22, (iv) a = 451, b = 33, (v) a = 484, b = 451.
2.39. Prove that gcd(ad, bd) = dgcd(a, b).
2.44. Does the Diophantine equation 12x + 33y = 1 have an integer solution? If so, can you list all integer solutions?
2.47. For nonzero integers a, b, c, gcd(a, b, , c) denotes the largest integer that divides all of them. Show that gcd(a, b, c) = gcd(a, gcd(b, c)).
In: Advanced Math
Coding: Use MATLAB to figure out the following problem, if you do not know how to use MATLAB then please do not answer. Coding is required for the exercise.
For f(x) = arctan(x), find its zeros by implimenting Newtons method and the Secant method in Matlab. (Hint: Use Newtons method to calculate x1 for Secant method)
Comment all code please since I would like to learn how to do this correctly in MATLAB. Thank you.
In: Advanced Math
Let V be the vector space of all functions f : R → R. Consider the subspace W spanned by {sin(x), cos(x), e^x , e^−x}. The function T : W → W given by taking the derivative is a linear transformation
a) B = {sin(x), cos(x), e^x , e^−x} is a basis for W. Find the matrix for T relative to B.
b)Find all the eigenvalues of the matrix you found in the previous part and describe their eigenvectors. (One of the factors of the characteristic polynomial will be λ 2+1. Just ignore this since it has imaginary roots)
d) Use your answer to the previous part to find all the eigenvalues of T and describe their eigenvectors. Check that the functions you found are indeed eigenvectors of T.
In: Advanced Math
Consider the lattice of real numbers in the interval [0,1] with the relation ≤. Does this lattice have any atoms?
In: Advanced Math
Karon went to the post office and spent $31.57 on 84 stamps. She bought 27¢ stamps for all the postcards, 42¢ stamps for each letter addressed to friends in the U.S., and 94¢ stamps for each letter to England. Karon bought 7 times as many postcard stamps as those for the letters to England. How many postcard stamps did Karon buy? (Hint: Use matrices.)
In: Advanced Math
You need to complete the following SWOT analysis:
Math Study Strategies 
Strengths 
Weakness 
Opportunities 
Threats 
Warm Up for Math class 

Learn new material first 

Study Breaks 

Learning Resources 

Group Study 

Flash Cards 

Review notes after class 

Write down important concepts after completing homework 

Ask your instructor for help 
In: Advanced Math
Creative Computing sells a tablet computer called the Protab.
The $780 sales price of a Protab Package includes the
following:
Required:
1. & 2. Indicate below whether each item is a
separate performance obligation and allocate the transaction price
of 100,000 Protab Packages to the separate performance obligations
in the contract.
3. Prepare a journal entry to record sales of
100,000 Protab Packages (ignore any sales of extended
warranties).
Complete this question by entering your answers in the tabs below.
Indicate below whether each item is a separate performance obligation and allocate the transaction price of 100,000 Protab Packages to the separate performance obligations in the contract.

In: Advanced Math
y_{1}(t) = (1+t)^{2} is a solution to y'' + p(t)y' + q(t)y = 0. Find a second solution that is linearly indepentent of y_{1}(t).
In: Advanced Math