1) For each of the following integral equations, classify as Fredholm, Volterra, or Volterra-Fredholm integral equation and find its kind. Classify the equation as singular or not. u (x ) = cos(x)+ (x-)'u(t)dt u(t) dt i) e* %3D ii) x-t

Q: 17-18 Find the differential of each function. 17. Answer dy Answer dy a. y = tan √t sec² √t 2√t b. Y…

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Q: sin(x²)y"-(cosx)y'+x²y = y'-3 y"+5xy'-3y = cosy

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Q: Given the composite function y=lnu,u=cosx. Express the differential of y in an invariant form.

A: We have been given a composite function. Let's call y = ln(u) as the outer function and u = cos(x)…

Q: List the six orders in which the three differentials dx, dy, and dz may be written.

A: First type= (dx)(dy)(dz) Second type=(dx)(dz)(dy) Third type=(dy)(dx)(dz)

Q: Find the total differential of the function z = y³x³ + 15y + 14. dz = Now calculate Az and dz for x…

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Q: Compute the differential dy for y = (2x + sin x)². dy =

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Q: u(x) = +2x sinh(z/4)− x |, etan''u(t)dt.

A: note :  As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find the chiftes ki,ke, ks) = then

A: The given question belonging to the calculus in which we have to find the total derivative of the…

Q: DATE Find the differential of the given function. ose the best answer a) dy: -x) dx xp (x-1)

A: here option B is true

Q: 1. Find the differential of w = x cos y – y sin x.

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Q: Express a general solution to the given equation using Bessel functions of either the first or…

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Q: Determine which of the differentials (or both) is the total differential: a) 2[cos(2x+2y²) + x ] dx…

A: a) 2[cos(2x + 2y²)+x] dx - [4y sin(2x + 2y²) + 1] dy is not a total differential, because it is…

Q: Solve the Schlömilch's integral equation 4. u(r sin t) dt, -T SIST. 1+x =

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Q: Identify whether the following differential equations are linear or nonlinear. State the order of…

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Q: R = aß6 cos(y) :) da + +([ X : ) ap + ( [ X

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Q: Compute the differential dz of the function. z = a°!l 9,,11 dz

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Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: Show that whether if the co-vector w can be written as dø differential? w = y. (x +). dx + x. (+).dy…

A: Given:  w=y·x+y2· dx+x·x2+y·dy....(1)

Q: (b) Determine whether u(x,t)= e' sinx is a solution to L

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Q: A) Find the total differential DZ (x,y) of the following function: Z= cos (3x² - y²)

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Q: Classify the following differential equation: e* + 3y = x²y dx a) Separable and homogeneous b)…

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Q: Show that the differential form in the integral is exact. Th (1,2,3) | 2xy dx + (x² -z°) dy -6yz dz…

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Q: Evaluate the curve f(x, y) = 0 which passes through the point (0,4) and satisfies the differential…

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