(7) (a) Compute the general solution of the differential equation y (4) + y" +y" - 6y + 4y = 0. (Hint: r4+²-6r+ 4 = (²-2r + 1) (² +2r+4).) (b) Determine the test function Y(t) with the fewest terms to be used to obtain a particular solution of the following equation via the method of unde- termined coefficients. Do not attempt to determine the coefficients. y(4) + y" - 6y + 4y 7e+ te cos(√3 t) - etsin(√3 t) + 5. =

Q: -8 X (x²+4)³/² -dx (use proper notation)

A: Given: ∫-∞∞xx2+432dx We have to evaluate the given integral.

Q: 4. Let f: Z Z be defined by f(n) = 3n-1. Determine whether this function is 1-to-1 and/or onto.

A:

Q: y"-3xy=0

A:

Q: Determine whether an = limit if it converges. In (5n+2) In (2n-3) converges or diverges and…

A:

Q: Activity 6: Half, equal, or twice as? In OF, AB, BC, CD, BD and AC are chords. Use the figure and…

A:

Q: Use the direct computation method to solve the following Fredholm integral equations

A: Given: Fredholm integral equation: u(x)=-11+9x+x3+x4-∫0120x-30t ut dtTo find: The solution of the…

Q: ( O O None of the others 0 3e2t 2 O →) Let F(s) = 1 e 2t 2 e2t 2 @21 2 - 1 2 + - 3 t 2 1 s²-2 s Give…

A:

Q: a) b) | c) | ]Find the equations of the normal line to the given surface at the point (,1,-1). Find…

A:

Q: Solve the IVP: y(4) +2y"+y=0, y(0)=1, y'(0)=-1, y"(0)=0, y" (0) = 2

A:

Q: 3. Draw Venn diagrams for the sets (AUB) nC and AU (BNC). Do your diagrams suggest these sets are…

A:

Q: For the curve defined by r(t) = 3 cos (t)i + 3 sin(t)j + 5tk evaluate t S= | = ||*|| 7" ( )|| du to…

A: We have to solve given Questions.

Q: The following function is linearized around t=0. Select the linearized function. f(t)=K(g(t))1/2 ro…

A:

Q: Consider the surface described by the equation z = √√yell 2 b) | a) ] Find the equations of the…

A:

Q: Find the distance between u and v. (2, − 1, 3, 1), v = u = (2, 02√2 3 √13 √11 (1, − 1, 1, 3); = u ·…

A:

Q: Consider the vectors U₁ of R3. The vector v = {U₁, U₂} if x is: 10 O 3 02 O None of these X 8 Select…

A:

Q: Find the interval of convergence for the series:

A:

Q: X Question 7 Find the matrix for T(w) = projí where v = [−1 −4 −8]ª. DNE X

A:

Q: Find the optimum strategies for player A and player B in the following game. Find the value of the…

A:

Q: Draw a graph that is Eulerian but not Hamiltonian.

A: To draw a graph which is Eulerian but not Hamiltonian.

Q: 5. 2X + Se, X 奇 Xuite dt

A:

Q: 6. The matrix associated with the solution to a system of linear equations in x, y, and z is given.…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Consider the following. (Assume that the coins are distinguishable and that what is observed are the…

A: Given that two coins are tossed. (Assume that the coins are distinguishable and that what is…

Q: Consider the following matrix: A = -4 00 2 10 1 0 4 -10 0 1 4 -15 0 0 7 a) Find the distinct…

A:

Q: Use row reduction to find the inverse of the given matrix if it exists, and check your answer by…

A:

Q: What is the graph's vertex set V? V = {EX: W, X |} What is the graph's edge set E? E = {Ex: {w, x},…

A: The set of all vertices called vertex set.

Q: list.) D³ 18D2+81D DD-9 X

A: In the given problem we find the function that annihilated the given operator. I, e we find the…

Q: b C Enter the neighbors of vertex c. Ex: x, y, z What is the degree of vertex c? Ex: 5 What is the…

A: We are given the graph. We have to find degree and total degree of the given graph.

Q: Find a, b, and n in the expansion of (a + b)" if the first three terms of the expansion are 729,…

A:

Q: Integrating Factors Found by Inspection 5. (x²y²*² +ay)dx+(x™¹³y² +bx)dy=0. State the condition of…

A:

Q: 3 For the work be, determine the shortest (1) 5 </

A: Given: Graph of the network is given. To find: We have to find the shortest path of the network.

Q: In a game of dice, a pair thrown in the table, what is the probability of getting a total sum of 10…

A:

Q: Evaluate the surface integral. 116x² S is the part of the sphere x² + y² + z² = 36 that lies inside…

A:

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A:

Q: Show that the function f(x)=x4 + 6x +1 has exactly one zero in the interval 1-1 01 Which theorem can…

A:

Q: The set of vectors that form a basis are Linearly Dependent Linearly Independent Inconsistent…

A: DEFINATION OF A BASIS-: A SET OF VECTORS v1,v2,v3,..........vn IN A VECTOR SPACE V IS SAID TO BE…

Q: E-Loan, an online lending service, recently offered 48-month auto loans at 3.6% compounded monthly…

A:

Q: Consider the region bounded by y=ln(x−1), y=2-x and x = 4 (see the figure on the right). a. Setup…

A:

Q: [3x₁ → R² be a linear transformation defined by L [X₂] = [3x¹+-+ e matrix representation of L, A,…

A:

Q: 20p. Using only one artificial variable R (to be used in the second constraint), setup the starting…

A:

Q: Tabulate and plot enough points to sketch a rough graph of the equation r = 7 -7 sin 0. Choose the…

A: The graph is defined as the pictorial representation of the set of data. The graph is basically in…

Q: Select ALL sets that are not subspaces of R². The set containing the points on the graph of the line…

A:

Q: 4) Use the superposition principal to draw a graph of each. a) y = f(x)+ g(x) b) y = g(x)-f(x) f(x)…

A: Given: Graph of the functions fx and gx are given. To find: Using the superposition principle we…

Q: Evaluate the following intergral: 0 512 8 S 1 3 y4+1 dy dx

A: Order of change of Double integral

Q: Find a vector a with representation given by the directed line segment AB. A(4, 0, -1), B(4, 3, 4)…

A:

Q: prove that f(x) = x sin√x is not [0,00) uniformly Continums

A: fx=xsinx We have to show fx is not uniformly continuous on [0,∞)

Q: If n = 12 m (me N), prove that "C₂ (2+√√3)² "Co- - + "C4 (2+√√3)4 "C6 (2+√3)6 ·+···=(−1)| 2√2 1+√3 n

A:

Q: When the determinant of an n x n matrix A is zero, which of the following must be true? Every row of…

A:

Q: If C is a circle of radius 6 centered at the point (3, -1), then evaluate f (4y - e³in (2)) dx +…

A:

Q: Find a basis for the column space and the rank of the matrix. 4 2 -3 -6 14 7 -6 -3 -4-2 1-2 4 2 -2…

A:

Q: a. Approximate the given quantity using Taylor polynomials with n=3. b. Compute the absolute error…

A: