Use Laplace transforms to solve the integral equation ...... ..... y(t) = 31² - e²² - fy(T)e y (T)et-TdT. A

Q: Find a harmonic conjugate of the function u(x, y) = arctan(x/y)− 6

A: Solution :-

Q: S e-t cos(e-t)dt 3.

A: we need to integrate ∫0πe-tcose-t dt   we can do this integration by substitution.

Q: Differentiate. (Assume c is a constant.) w3/2(w + ce") 3 z' = e" w W.

A:

Q: Tte ne-(s+a)t dt

A:

Q: Solve the equation: (dy/dx) + (3y/x) + 2 = 3x, y(1) = 1. %3D

A:

Q: Find the differential dy of the function y=-2²-3x - 2. Select one: O a. (-x-3)dx. O b. (-2x - 3)dx O…

A: dxndx=nxn-1d(constant)dx=0

Q: Find the velocity, acceleration, and speed of a particle with position function r(t) = (-2 cos t,…

A:

Q: Find r'(t). cos 4 cos³(t)i + 2 sin³ (t)j + k r(t) = 4

A:

Q: Find the domain of r(t)= (sint)i+ln(6–t)j+ Vt+ 2k.

A: Given :rt=sinti+ln6-tj+t+2kWe need to find the domain of the function rt.

Q: Differentiate. g(t) =  5 − 7t 8t + 9 g′(t) =

A: solution: the objective is to find the derivative of the given function

Q: A. Find the derivative of the function at o P in the direction of A f(x, y) = x V3sec-1(2xy)at P.…

A: To find the derivative of given function means we have to find the directional derivative of the…

Q: Find the differential dy of the function y = 4x²-x+ 3 Select one: O a. (8x-1)dx O b. (x²-x² + 3x) dx…

A: Solve for the differentiation

Q: dx V2x – x2 arcsin(x – 1) + c -

A: