Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) = x₂ using the following values. 4t [² =2]·--[*]-×-[8]·~^-[ x(0) A = x(t)= f(t) At cost + 2 sint sint - 5 sint cost-2 sin t

Q: A coin sold at auction in 2019 for $3,158,000. The coin had a face value of $2 when it was issued in…

A:

Q: 1. y" + 5y + 4y = 5e4x + 4, y(0) = 0, y'(0) = 1

A:

Q: The population of bacteria in a culture grows at a rate proportional to the number of bacteria…

A: Let, be the population size of bacteria at time t.Then according to given information, ,where  is…

Q: Use Separation of Variables on the following partial differential equation: ∂u/∂t = k(∂^2u/∂x^2),…

A:

Q: Use the method of variation of parameters to find a particular solution y, of the Up differential…

A:

Q: can you guys do vi

A: The eigenvalues of a square matrix have upper and lower bounds thanks to the Gershgorin's Circle…

Q: Let's work with a quaternion q representing a rotation of theta = 40 degrees around the axis n-hat=…

A: Given that rotation angle degrees and the rotation axis: -hat The objective is to find the second…

Q: Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 14 4 6…

A:

Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a)=x₂…

A:

Q: f(x) = Error in solution (line 11) y_theta-double(f(x_theta)) Output x0 = Commands Unrecognized…

A: Given the following output in the command window,You have defined x0=4. Instead, use the…

Q: ® let Act show that the eigen Value d of A are the diogenal elementa and b

A: According to Bartleby Guidelines ,we solve only question number 3.The given matrix is .Also a and d…

Q: Find f(t). f(t) = 2- 1 (s – 4)3 ]

A:

Q: Carmine is creating a schedule for five key presenters who will be speaking to students on career…

A: The persons speaking to students on career day are…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Find monotonicity, convergence or divergence, and bounds (if…

A: Monotonic sequence : A sequence is called Monotonic if it is either increasing or decreasing as n…

Q: find a basis for the mullspace of the matrix A and find the dimension of that space. A= -3 2-62 3-93…

A: The null space of an  matrix A is

Q: b) an = 2an-1-an-2 with ao = a₁ = 2 a1

A: Given recurrence relation

Q: Evaluate each integral. "In(x) xe dy = e (In(x) [the [incx). xey dy dx = 82 (in(x) $6hxe xe dy dx…

A: We have to evaluate the given integration.

Q: 2. Let me N and a € Z. (a) If ged(a,m) = 1, then Bézout's lemma gives the existence of integers x…

A: As asked we shall solve only question 2. (a).Let .(a) If gcd(a, m) = 1, then Bézout's lemma gives…

Q: Which of the following is the orthonormal basis formed using the Gram-Schmidt process on the…

A: The given vectors are:

Q: (22) Define X(t) := w(s) ds, where W() is a one-dimensional Brownian motion. Show that E(X²(t)) = ==…

A: Given,To show that E(X^2(t)) = (t^3)/3 for each t > 0, where X(t) is defined as X(t) := ∫W(s)ds…

Q: 5. Find all the physically relevant steady-states of equations (1)-(2), stating their bio- logical…

A: note :As per the instructions we will only solve part (5) of the question.As per the question, we…

Q: pive the following homogeneous system of linear equations: 1-5x2+10x3 = 0 3x₁+3x₂-6x3 = 0…

A: Augmented matrix of the given system

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y'' +…

A:

Q: -{] Let W be the union of the first and third quadrants in the xy-plane. That is, let W = a. If u is…

A: This question is about to check vector space.

Q: Solve the following nonlinear ODE dy dx y 2x X الله

A: We have to solve the nonlinear ordinary differential equation      ......(1)We know thatIf ode is of…

Q: Determine whether the following are subspaces of R2×2: The set of all 2 × 2 triangular matrices

A: The set of all 2 × 2 triangular matricesTo determine whether it is a subspace of .

Q: Solve the exact ODE (2y²x - 3) dx + (2yx² + 4)dy = 0

A:

Q: Prove that the permutation symbol (e) defines a Cartesian tensor in R². It is assumed that e is…

A: Given:To prove that the permutation symbol defines a Cartesian tensor in .

Q: Calculate the double integral of f(x, y) = 48x over the triangle with vertices O = (0, 0), A = (3,…

A: The function .We have to calculate the double integral of over the triangle with vertices .

Q: A trust fund with a beginning balance of $35,000 earns interest at 3.0% compounded quarterly. If…

A:

Q: Predict the population of the country in 1994. Include units. Round to the nearest whole number.

A: The base year is

Q: 7. Let {an1 and {bn}1 be convergent sequences with limit A and 0, respectively. If bn 0 for all n N…

A:

Q: The auxiliary equation for the given differential equation has complex roots. Find a general…

A: Solution:-  Given that the differential equation                     The given differential equation…

Q: Use the method of variation of parameters to solve the initial value problem x'=Ax + f(t), x(a)=x,…

A:

Q: 1. The summation below can be used to approximate an area below (c) Draw the rectangles on the…

A:

Q: Let V₁ = (1,0,0), V₂= (2,2,0), and V3 = (3,3,3). (1) Show that the set S={{V₁, V₂, V3} forms a basis…

A:

Q: 13. Re-parametrize the curve with respect to arc length measured from the point where t = 0 in the…

A: In this question we Re-parametrize curve with respect to arc length.Note: As per our Guidelines we…

Q: (8 points) f(x)-3-x a) lim f(x) = 100 √√ ifx3 d) lim f(x) = x-3' e) lim f(x) = f) lim f(x)= x-3

A:

Q: for part b of the question, how did we get 2 answers after isolating for x?

A: Since the sinusoidal function is periodic , we get the repeated value.We can clearly see this in a…

Q: 52 percent of students are male. 34 percent of students take statistics. 38 percent of male students…

A: Given  percent of students are male. percent students take statistics. percent male students take…

Q: Q₁:A. Solve the ODE: x³y"" - 3x2y" + 6xy' - 6y= 10x² use the variation of parameters method to find…

A:

Q: Find the equation from the graph. *P M N Q a N 1 A. y=x-4 O B. y=4x-4 OC₂ y=4x+4 C. OD. y=x+4

A: A graph of the linear function is given.We have to find its equation.

Q: D, E, and F own a business jointly and share profits and losses in the same portion as their…

A: D, E, and F own a business jointly and share profits and losses in the same proportion as their…

Q: Find a particular solution to the differential equation using the Method of Undetermined…

A:

Q: 0 f(x) = { f X 0 -2≤x≤- 1 -1 < x < 1 1 ≤x≤ 2)

A:

Q: Definition. A ring R with identity 1, where 1 # 0, is called a division ring (or skew field) if…

A: A ring  with identity  where , is called a division ring (or skew field) if every nonzero element…

Q: Consider the following Gauss elimination: What is the determinant of A? det (A) = Γ1 0 77 A 0 1 0 A…

A: The elementary transformationsWhere

Q: Without actually solving the given differential equation, find the minimum radius of convergence R…

A:

Q: Let f be a convex, differentiable, L-Lipschitz function where L = 3. Let æ* be the global minimum…

A:

Q: Consider P2 and the set S = {2x + 3x², -1+3x+x², 2 - 4x + x²}. What is the coefficient matrix for S?…

A: