DIFFERENTIAL EQUATION 1. dy+2x²y=2xe* dx 2. az -x²cosy-w ay 3. ax² d'x d'x\/d³x dt dtª dt³ +X=t 4. 13/4 √√₁. (X²)² - [ COS X + (x²)* "* 5. x sin(1+ y)= 3y (4-x²) TYPE ORDER DEGREE LINEARITY DEPENDENT INDEPENDENT VARIABLE VARIABLE

Q: Consider the following vectors: --0-0-0 W2 = -5 1 = -2 Enter the vector projwv in the form [C₁, C2,…

A:

Q: 16. What is the domain of the given function f(x)= 5 x-14 +10? A. {x|x€ R} B. {x|x #14} C. {x|x 10}…

A:

Q: fo (1) ((e-st) cos(1) ✓ ) at V dt 0 £{f(t)} =

A:

Q: Compute the flux of the vector field (x¹, — xy³), out of the rectangle with vertices (0,0), (4,0),…

A: Given vector field is (x^4,-xy^5). The flux is given by flux=∮CF⋅n…

Q: Graph the parabola y = x2 + 1 by plotting any three points on the parabola. Move the key points on…

A:

Q: Find the particular solution. dy y dx X + 1+ y X ; when x = 1, y = 8 C

A:

Q: Find a number x between 0 and 90, such that x ≡ [4,8] mod [7,13].

A:

Q: Use the quadratic formula to solve the equation. 2x²-13x = 1 ... The exact solutions are x =…

A: The approximate and exact solution

Q: Consider the following. x = 3 cos(8), y = sec²(0), 0≤0 < 1/12 (a) Eliminate the parameter to find a…

A:

Q: dx x²√4x² O a. √4-x² 4x √4+x² X + C + C O b. O d. 4x √4-x² X /4+x² + C + C

A:

Q: Suppose that the population of whales in world’s oceans increases by 20 % per year in the absence of…

A:

Q: (Find the family of solutions of the separable equation): (x − 5)y² – ²²(y² — 4) - a) In r+-+=y=0 b)…

A: Given, x-5y3-x2y2-4dydx=0

Q: Find  C(n, x)pxqn − x for the given values of n, x, and p. (Round your answer to four decimal…

A:

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

A: Since there are two questions, therefore find the solution of the first question.

Q: Given that f(x) = 4x + 5 and g(x) = x² - 2x - 5, find (gof)(-7). (gof)(-7)= (Simplify your answer.)

A:

Q: 1. If u(x, y, z) find = 21 v(x, y, z) Jºu əx³əy² əzª x³y³ 25 and ე10 əx¹ Əy¹ əz² and w(x, y, z) Jw…

A:

Q: 11. u(x): + f² = cos x + K(x, t)u(t)dt, K(x, t) = 6t(1), 6x (1 – t), for 0 < t < x for x < t <1

A:

Q: Find the particular solution. dy y y dx=2+ 1+ ; when x = 1, y = 8 X X L

A:

Q: (b) The Laplace transform of the function g(t) = OA OB. 483 (8-e)4 384 G(s) = G(s) = fe-e 6 is

A:

Q: 2. For each of the following functions decide whether it is one-to-one and whether it is onto, and…

A:

Q: 1,-3, 4, 1, -3, 4, 1, −3, 4, ... In the sequence above, the first 3 terms repeat without end. What…

A:

Q: 4. If the function f(x, y) is given by f(x, y) use Taylor's formula for f(x, y) to find the…

A: The given problem is to find the quadratic approximation of the given function near point (0,0)…

Q: QUESTION 20 Is computing the interest as fast as possible (e.g., by the second) a realistic way of…

A: It is not realistic way to compound intrest  by the second  . Hence answer is False

Q: If f'(x) = g'(x) on the interval (a, b), then f(x) = g(x) on (a, b). O True O False

A: We find counter example of f(x) such that f'(x)=g'(x) but f(x) ≠g(x) on (a,b).

Q: Suppose T: R³-R² is a linear transformation. Let U and V be the vectors given below, and suppose…

A:

Q: 3. Find the Taylor series of the function f (x, y) = e-*cos(2y) - 7 at the point (ln(2), 0) up to…

A: The given problem is to find the second order Taylor polynomial of given function of two variables…

Q: Let g: R^2 -> R be defined as g(x,y) = XY for all (x,y) an element of R^2. Describe g^(-1) ([-1,1])…

A: Given, g: ℝ2→ℝ gx,y=xy, for all x,y∈ℝ2 g-1-1 in -1,1 subset of ℝ2 ∴x,y=g-1xy ∴xy=-1 in -1,1 subset…

Q: Find a basis B for the span of the given vectors. 3 0 HG 0 1

A:

Q: Find the product: ** L 2 7 -5 -6 -8 -10 1 -7 8 100 0 1 0 001 =

A:

Q: Find the values of x for which the series converges. (Write your answer using interval notation.)…

A:

Q: 3-Express the number 2345 in base 6. Express the number 2700 in base 16.

A:

Q: Consider the following. X lim X-0 Create a table of values for the function. (Round your answers to…

A: Consider limx→∞sin2xxTo estimate the limit and complete the given table.

Q: Evaluate the integral by making an appropriate change of variables. 5 cos (5 (=)) da dA where R is…

A:

Q: Consider the matrix A = 1 1 P = Let x = 1 √2 1 √2 0 -|-~| 1 √6 1 Compute [x]. √6 2 √6 1/11/11/1 I 2…

A: Suppose B =12120, 16-1626, 13-13-13 and x=-43-1And let xB=abc

Q: By dragging all of the statements from the left column to the right column below, display a complete…

A: The given integration is : ∫25 x2dx It can be written as: ∫25 x2dx=limn→∞∑k=1nf(xk)△x   ,where f(xk)…

Q: r, s, and t are three consecutive odd integers such that r<s<r. Quantity A r+s+1 Quantity B s+t-1 A…

A:

Q: (b) Check all of the following that are true for the In(2n)+3n n² series Σ n=1 A. This series…

A: Series and sequence

Q: 1. Solve the following differential equations using variation of parameters. If no solution is given…

A:

Q: In a recent year, an author wrote 174 checks. Use the Poisson distribution to find the probability…

A: Solution :-

Q: Use the given information to find the number of degrees of freedom, the critical values x2 and x2,…

A: Given, 98% confidence n=27s=0.24 mg

Q: n is a positive integer, x=7n+2, and y=6n+3. Quantity A The ones digit of x + y Quantity B 5

A:

Q: Let B = {V1, V2, V3, V4} be a basis of Rª given by the following vectors: 2 2 ·¤ , V3 0 2 Use the…

A:

Q: Suppose we wanted to use mathematical induction to prove that for each natural number n Σ(3n-2)…

A:

Q: A new revolution in research that encourages collaboration, the sharing of data, and the ability to…

A:

Q: Express the function f(t) = 0 t 6 in terms of unit step functions and hence determine F(s), the…

A:

Q: 4 6 8 10 12 ਨ (2,-6) (A B 12 The graph of y = f(x) consists of a semicircle with endpoints at (2,…

A:

Q: For each of the following, if the Inverse Function Theorem applies to f at c, find Dg(x, y) both…

A:

Q: Exercise 2 Let X be a topological space. 1) If A CX is dense in A, show that, for every open subset…

A:

Q: IT i=1 3 - 레페루 = (2) |T|| U

A: The conjugate gradient method is a mathematical technique that can be useful for the optimization of…

Q: 1. Prove by induction that for every n ≥ 1 we have 1 2n (2n + 2) 1 + 2.4 4.6 + + = n 4(n + 1)

A: 12·4+14·6+....+12n2n+2=n4n+1 Let Pn=12·4+14·6+...+12n·2n+2=n4n+1