if J, and J', are Bessel functions then J, is given by -2J 1.a O .b O Jo -J' 1.d O

Q: Determine fry when f (x, y) = x sin¬' () -1 1. fry = (x² – y?)3/2 y? x² – y? 2. fry - xy 3. fry (x²…

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Q: If u = x² cosy+ ye", where x = s+2t and y = st, prove that ди ди 2- (s – 21) (x siny- xye – e"). -…

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Q: By the odd extension method applied to the function f(x)=e-2=, where r > 0, the Fourier integral of…

A: Given function fx=e−2x where, x>0 We have to find the Fourier integral by the odd extension…

Q: 2. (a) Let f(x, y) = x² sin(x + y), find 잃 and 잃.

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Q: Prove that the following ODE is exact and find the general solution dy (2xy + 1) + (x² + 3y²) dx

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Q: Find the Wronskian for the set of functions.{1, sin 2x, cos 2x}

A: Here the given function  {1, sin 2x, cos 2x}

Q: 1. If y= tan x, prove that y"= 2(y² +1)(3y² +1).

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Q: (a) Find if y = y (ln r). (b) The function f(z) (In r) is an invertible function (you do not need to…

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Q: Suppose that S"(ax + b) cos x dx then the value of a equals

A: Given,           ∫0πax+bcosxdx=6To find: The value of a.

Q: C. If w=f(x,y) and x = r. cose, y=r. sine. Prove that aw ar aw +1 (2001) = fx² + fy²

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Q: lue of c is the following function co: CO In (cxy+1) if (x, y) + (0,0) 4) = ху

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Q: If r (t) = (sin(t), cos(t), 2), then ſr (t) dt = 0.

A: The vector function is given by rt = sin(t),cos(t),2 To evaluate : ∫0πrtdt

Q: 9 Floy : 2vin8t y co)= 2

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Q: If x, y and z are independent variables and f(x, y, z) = x sin(y + 3z) of then find ôz .

A: Here, x,y,z are independent variables. Given function is f(x,y,z)=xsin(y+3z)

Q: 2. Evaluate these derivatives BJ(J+1) ON calculate aJ a) Given N = (2J +1)e RT

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Q: If F(x,y,z)=sin(x³y²)+cos (Vxy2)+x®y²z, then fyz(1,-2,1)=

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Q: Pron a. If u = f(x, y), where r = e' cost, and y = e' sint, show that (3)³ + (3) ² - - ² [(-)* +…

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Q: (b) Show that, the function u = In(x² + y²) + 2 tan" satisfies Laplace's equation.

A: A Laplace equation is a 2nd-order partial differential equation. This is defined by,…

Q: If S", f(x) cos(mx)dæ = } g ar cos(n²a) f(x) = Ln=1 nt +1 then m =

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Q: Suppose that z is a function of z and y and that ze y cos z. Find and

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Q: H.W: if w x2 + y2 + z2, x= e*Cos6, y-erSin0, z=e0 prove that aw/ar= er/w and aw/a0 = e20/w

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Use the variation of parameters to find the general solution of the following ODE. z'' + z = tan2 x

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Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: Suppose z = x² sin y, x = 3s² +lt², y= 2st. A. Use the chain rule to find and as functions of x, y,…

A: Consider:z=x2sin y, x=3s2+t2, y=2st. A1) Find ∂z∂s. Apply chain rule ∂z∂s=∂z∂x·∂x∂s+ ∂z∂y·∂y∂s Find…

Q: 1. Find ar, aN, N, T, and k for: (a) F(t) = (5t, t, 4t) at the point (10, 4, 8) (b) ř(t) = (1 – 2t²,…

A: (b) Given rt→=<1-2t2,2-t2,t3> and given point is -1,1,-1. Therefore by comparing, we get…

Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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Q: (a) If t = 0, sint = and cos t = (b) If t 4' sint = and cos t = (c) If t = 2' sint = and cos t = 37T…

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Q: (d) п x — а)", b>0 bn n=1 (e) The Bessel function of order 0 (-1)"x²n 22" (n!)2 Jo(x) = £ n=0

A: We have to find the Radius and interval of convergence of series.

Q: Let z be defined implicitly as a function of r and y by the equation dz 4+ In (ry) – cos (cy – 2) =…

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Q: 1. If Z = sin r+ 2 I+1 6. - ", find dZ/dr.

A: differentiate with respect to x

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

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Q: (b) Find an operator A that annihlates the following functions. i. In(x) ii. to , α ε R iii. sin(3…

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Q: Let z be defined implicitly as a function of x and y by the equation dz 4+ In (xy²) – cos (xy – z) =…

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Q: 2n Jnsi (x) = " J,(x) – J(4)

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Q: If z=1+y , I= e' cos(s) and y=e' sin(s), then at (t, s) = (1,0) is as O-2e O 2e O 2e

A: if z=x2+y2 where x=et coss , y=et sins then find ∂z∂s at t,s=1,0

Q: Find F' if rsin ) = /" 4 nin" t t. F(x) = cos-lr

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Q: If f(x,y,z)=In(x²y+sin?(x+y))+111x112y2z113, then at (1,1,1) is equal to əx²əyəz

A: We have to find derivative

Q: - Show that the following functions satisfies the heat oquation = . (e>0, constant). 1)2 =e sin .…

A: Since you have posted multiple questions, but according to guidelines we will solve first question…

Q: 15. Determine if the given functions are linearly dependent or independent. (Prove your answers) {e…

A: 15.  a) Given, e2x, 3x Now the Wronskian is, Wf, g=fxgxf'xg'x=e2x3x2e2x3=3e2x-6xe2x≠0 Since the…

Q: -1 If cos x+cos y+cos z= T, prove that x +y +z +2xyz = 1

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Q: Suppose u = er sin (p), p= sin(3x), q = z² In(2y) , and r = ?. Assume that –7/6 < x < «/6. Compute…

A: Partial differentiation is termed as the differentiating function with respect to the single…

Q: Let f(r, y, z) = In(x² + 2) + y?e - cos(2y2). Find feyr-.

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Q: (f) If w=4x² +4y² +z² ,x= p sinø cos0, y= psinøsin0 , z =pcosø, Əw find and ap

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Q: 1. If y= tan x, prove that y= 2(y´ +1)(3y² +1).

A: Use the following differentiations as, ddx(tanx)=sec2(x)ddx(sec(x))=sec(x)tanx Now, differentiating…

Q: Find f(4) if Jo f(t) dt = x cos Tx.

A: Here given as ∫0xftdt=x cos πx Difeerentiate with respect to x ddx∫0xftdt=ddxx cos πxfx=xddxcos…

Q: 2,5 Given f(z, y) sin(x + y) where 2s 5t. Find f.(ar(s, t), y(s, t)) f(x(s, t), y(s, t)) =| Note:…

A: It is given that f (x, y) = sin (x + y) where x = s2t5 and y = 2s–5t.

Q: 1- Find dwi dt at the given value for w ==+2,x = cos (1), y = sin (1),z = w =-+ at = 3

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Q: If f(x, y) = e“ sin(4y) then: 4 sin (4) 4 cos( 4) V f( – 1, 1) . el el

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Q: 1 Use the substitutions given to find fI+x dx; u = 1 + x + sin x dx; u = sin x cos x a

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