Evaluate the value of I = f(e²¹ − 6x)dx + (2xe²y + y)dy, where C is the parabola C y = x² - 4x from (0, 0) to (4,0).

Q: Find the flow streamlines associated with the indicated complex function. f(z) = iz

A: Given: fz=iz. We have to find the flow streamlines associated with the given complex function.

Q: Find all harmonic conjugates of u(x, y) = x³ - 3xy² + 2y.

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Q: A function y = f (x) is represented parametrically as follows: x= (t)=t-5t- 20t +7 y = v (t)=…

A: We will find out the corresponding extremum for given function. Kindly note that there is a misprint…

Q: Please solve

A: Consider the function

Q: y + 2xy). Find values of a and b so that f (x + iy) will be analytic. Consider the complex-valued…

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Q: xy² dA, R = [0, 2] × [- 3, 3] Find x2 + 1 R

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Q: b) Evaluate the value of I = S(e³y – 3x)dx + (6xey + y)dy, where C' is the parabola - C (0, 0) to…

A: One has to solve it by Green's Theorem.

Q: Find the change of variable x = Py that transforms the quadratic form x¹ Ax into y¹ Dy as shown. -…

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Q: 2. d-4 d+9 2d a²+3d-28

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Q: Find an equation that repesents C(t) = -2i + 3eit, 0 ≤ t ≤ 2π but traveling in the opposite…

A: Equation travelling in opposite direction

Q: Solve: (x+y)dy-(x - y)dx=0 A. x² - 2xy-y²= B. x² + 2xy + y² =c C. x² + y² =c D. x² - 2xy + y² =

A: The given equation is(x+y)dy-(x-y)dx=0 To solve the differential equation.

Q: dy as a function of x. Write the function in the form y = f(u) and u= g(x). Then find y = (- 2x +8)…

A: We know that ,  if y = f ( u ) and u = g ( x )  Then  dy / dx = f ' ( u ) • g ' ( x )

Q: Determine for which values of m the function (x) = xm is a solution to the given equation. d²y dy -…

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Q: Sketch c(t) = (t3 − 4t, t2)

A: This is in parametric form. So we will convert it in normal form.

Q: Question #49 in the picture. Differential equations

A: We are given the differential equation,

Q: c) Show that y(x) = 1+ax+bx², where a and b are non-zero, is a solution to Laguerre's equation, d²y…

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Q: Verify that the function u(x.y) x- 3xy -5y is harmonic in the entire complex plane ,And find the…

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Q: h the comp y² + 2xy)

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Q: Evaluate / (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (7, -5)

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Q: Find an equation that repesents C(t) = -2i + 3eit, 0 ≤ t ≤ 2π but traveling in the opposite…

A: Equation in opposite direction