Integrating Factors found by inspection y(x²y²m)dx + x (x²y²+n)dy=0 when x = e, y = 1 y(x² + y²-1)dx − x(x² + y² + 1)dy = 0 when x = 1, y = n (x"y"+¹ + ay)dx + (x"+¹y" + bx)dy = 0 state the condition of the general solution when n÷0 and n = 0

Q: 1² + 1 2. Find the equation of the tangent line to the graph of F(x) = sin^ ¹ (1) + m² dt at x = 0.

A: Fx=∫1-2x1t2+1sin-1t+πtdt,   x=0

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = x³i + y³j+z³k out…

A: Given : F→x, y, z=x3i+y3j+z3k x2+y2≤4, 0≤z≤3 To find: ∬S F→ ·dA→

Q: For each of the relations ~ on the integers ~ is relation, explain your an equivalence following…

A: A relation on a set is said to be equivalence relation if it is reflexive, symmetric and transitive

Q: Let S be the portion of the cylinder x2 - 6x +z = 0, oriented by upward-slanting normal vectors,…

A: The given vector field is F = xy, 3xz2,yz.Our aim is to find the flux or surface integral of the…

Q: 08(3-j2) 7245

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Q: 37. Y (-4,0)(1, 0) 10x < 21 X 40. 3x² +

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Q: x+1 y-3 Find the equation of the plane containing line =

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Q: ries converges or diverg verify that the condit n² +3 Σ(1²2+3³3 2n² + 1 n=1 72

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Q: 1² + 1 1-2r sin ¹(t) + x² 2. Find the equation of the tangent line to the graph of F(2) = ₁2 s dt at…

A: Equation of the tangent line to the curves

Q: The folloiwng illustration is drawn scale. X = y= 80 ft 53 ft A = X 133 ft y Find the Missing…

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Q: Solve the given initial-value problem. X(t) = -1-2 × = (-¹-²)× + (2), ×(0) - (-²) X' X 3 4

A: X'=-1-234X+44, X0=-24

Q: 3. Pick an interesting positive integer a with a > 20. 1 (a) How many nonnegative integer solutions…

A: It is given that a&gt;20. (a) The objective is to determine the number of nonnegative integer…

Q: 64 If y = cos ax, prove that У У1 У г Уз У4 У5 |=0, where y Уб У7 Ув d' dx' у.

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Q: Determine L{"e3r cos(t-7)dr} 0 Select one: (8+3)(82+1) 8 (8+3)(82-1) 8 (8-3)(82+1) 8 (8-3)(82-1)

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Q: Find an orthogonal basis for the column space of the matrix to the right. -1 7 1-7 1-3 1-3-2 6 4 6

A: The given problem is to find the orthogonal basis for the column space of the given matrix.

Q: 4. Consider the Cubic Equation: x³ +3x² = 8x +30 a. Reduce the cubic equation through a change of…

A: The given cubic equation x3+3x2=8x+30 can be rearranged to the standard form as: x3+3x2-8x-30=0 A…

Q: Determine the solution of the following differential equations. a) (D² +9) y = 81x² + 14cos3x b) (x…

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Q: 4. 5. Let A be the following matrix: A = -5 -5 0 0 4 2 0 0 0 0 0 0 1 0 5 -1 3 -5 -3 0 0 -1 - 0 1 1…

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Q: Problem II Consider a linear transformation L₁ : Rª → R³ given below and a linear operator L₂: R³ →…

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Q: 2 - i)₁ dz, 4 dz, r = {2: 2-1 - i| =

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Q: Solve the given initial-value problem using the Laplace transform: -{- = x(0) = 5. x' + 3x if 0<t<4…

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Q: Solve for DE xy' + (1 +×)y = e^-x sin(2x)

A: Solution of the linear differential equation

Q: Consider the complex number z given below in rectangular form, and marked on the complex coordinate…

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Q: Problem I Determine for which values of the real parameter a the following matrix is not invertible.…

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Q: Find the eigenvalues of the given matrix. -14 -6] 36 16

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Q: Given the first order initial value problem, choose all correct answers dy 2x-3y y(-1)=2 dr 4y + 3x…

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Q: z = ln(4-j7)

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Q: 4. Let R be an integral domain having field of fractions F (a) Define i: R→ F by i(a) = [(a, 1)].…

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Q: Solve the initial value problem of (y" + 4y = 6₂ (t)et ly(0) = 0, y'(0) = 0

A: Solve the differential equations using Laplace transformation

Q: Determine the solution of the following differential equations. e) y" + 4y' + 3y = cos(ex)

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Q: (4, 4, 5) (1, 1, 1) ܫܘ ܐܢܘܓܢܤܣܐ

A: Given the differential is exact , we need to find the value of integral

Q: Use fraction strips and number lines. 1. Use the number lines below. List all fractions equivalent…

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Q: Question 12 Compute the product or state that it is undefined. 5-3 || Undefined -3 4 -3 8 2 -4 8 [-2…

A: Remark: Let A and B are matrices of order m*n and n*p. Then multiplication of A and B is possible…

Q: Find the work done by F over the curve in the direction of increasing t. F = ti + = j + k ; C: r(t)…

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Q: A glass sphere given by the equation (x-1)²+(y-2)²+(-3)² = 36 is floating above the plane 2x + y -…

A: The given problem is to find the point on given sphere is farthest from the given plane. Given…

Q: Find the work done by F over the curve in the direction of increasing t. F = i + j + k; C: r(t) =…

A: We have to find the work done by F over the curve in the direction of increasing t

Q: a) Evaluate £{e5¹}. b) Evaluate L{(t− 3)² + sin 7t + cos 8t} c) Use the Laplace transform to solve…

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Q: The polynomial function f(x) = x³ + x + 1 is invertible - that is, th function has an inverse. (a)…

A: Given That : The polynomial function fx=x3+x+1 is invertible. To Find : a) Graph y=f(x) and also…

Q: If p is a natural number, then prove that p"+1 + (p+ 1)2n-1 is divisible by p² + p + 1 for every…

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Q: 1) A particle moves in a velocity field (²xy + 10, x²) starting from point (0, 1) at t = 1. Where…

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Q: F = V(xy6₂³); C is the line segment from (3, 1, 1) to (4, 1, -1) Hint: First calculate gradient of…

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Q: Solve the ODE (e³ + 1)²e-³dx + (eª + 1)³e-ªdy = 0, y(0) = − = -4 by separation of variables.

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Q: Find the value of T sin (77 14 sin 3π 14 sin 5T 14

A: We have to solve given Questions.

Q: Question 25 Calculate the circulation or line integral of the field F around the closed curve C. F =…

A: Given: F=y3i+x2j Vertices of triangles are (0, 0), (3, 0), and (0, 4). To find the line integral of…

Q: Find the area of the region enclosed by r = 2 + cos 0.

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Q: Find the surface area generated by rotating the given curve about the y-axis. x = ett, y = 4et/2, y…

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Q: Let T = (tij) be the 7 × 7 matrix with (i, j)-entry tij given by 1,1 ≤ i ≤6, tij 0 for all other i,…

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Q: 4. Solve dy d.x. 3y² - x² XU . Note: your solution may be left in implicit form.

A: Use variable separation method after y substitution to solve.

Q: Consider the following linear programming problem: Max Z=12 x₁ + 15 x2 s.t. 20 x₁ + 10 x₂ ≤ 60 X₁ +…

A: Here corner points are , (0,0), (0,3),(3,0),(2,2) At (2,2) we have optimal solution.

Q: Determine the solution of the following differential equations b) (x + 2y - 3) dx - (2x + 4y - 9)dy…

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