-[x(sec y+ tan y)-2ycos y] =0. Ans.: x(sec y + tan y) + y =c.

Q: Solve the following Exact DE using Method of Grouping. 2) (y sec?x + sec x tan x)dx + (tan x + 2y)dy…

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Q: Assume that x = x (t) , y = y (t) and z = z (t) and differentiate the given equation with respect to…

A: Assume that x = x (t) , y = y (t) and z = z (t) We have to differentiate the given equation with…

Q: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

A: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

Q: Find the area between the inner and outer ovals of the curve r2 = 16(2 – cos 0)

A: Given,

Q: Find the length L of the curve R(t) = e* cos(3t) i + e* sin(3t) j + 3e*k over the interval [1, 5]. L…

A: given: Rt=etcos3ti+etsin3tj+3etk interval 1,5

Q: (c) x(t) = eat cos s wtu(t), a > 0 (d) x(t) = e-af sin w,tu(t), a > 0 %3D

A: Let xt is a function. The Fourier transform of the function xt is denoted by Xiwor Xf and defined by…

Q: How would you verify that the following equation is not exact?(-xysin(x)+2ycos(x))dx + 2xcos(x)dy =…

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Q: Find the value of dy/dx at the point defined by the given value of t. x 5 sin t, y = 5 cos t, t= O…

A: Given, x =5sint  y =5cost We have to find the value of d2ydx2 at t = 3π4

Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

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Q: If z=x+ iy=r(cos(0) + isin(@)) then |:|=/x? +y² =rO arc z=0 Z=rO

A: By definition of modulus u got |z|=r

Q: Find the circumference of the curves x=e^-2θ (sinθ+cosθ), y=e^-2θ (sinθ-cosθ) over the interval 0 ≤…

A: To find: The circumference of the given curves. Given information: Concept used: If a functions are…

Q: Find the area between the inner and outer ovals of the curve r2 16(2 – cos 0)

A: To find the area between the inner and outer ovals of the curve

Q: 1- If e +x +y+arctan(z) = 2 then what is the value of dy da at (0,1) ? a) - 2 b)2 c)0 d 1 e) - 1 a)…

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Q: The general solution of + ytan x = sec x is dx A y = sec x + C sin x В у (sin x - 1) %3D С y= sin x…

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Q: Express in form y=f(x) by eleminating the parameter x = t , y = tan−1(t3 + et )

A: It is given that,

Q: Find the surface area of the figure generated by revolving x = 6 cos(t), y = 6 sin(t) where 0 <ts…

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Q: given sin -In\x+ y + 19| Ax, y) = V18 – (x + 11)² – (y + 10)² sketch domain p(-11+ v7, - 10) is…

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Q: 2. for, (x+y)X = tan-14x + TT* + dx dy a)- Find InIny

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Q: A particle moves in the xy-plane in such a way that its path is defined by x = e^t cos t and y = e^t…

A: Given that, x = e^t cos t y = e^t sin 2t Differentiating x with respect to t we get, dx/dt = e^t cos…

Q: .: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G (x, y) = x³ y² + y² sin…

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Q: If x = sin2 (u) and y = cos² (u), then dy is : dx а. 1 b. cot(x) C. tan(x) d. 1-

A: Differenriate

Q: x = a(0 – sin 0), y = a(1 – cos 0). %3D %3D urve followed by the particle as a function of 0.

A: The given parametric equations are, x=a(θ-sinθ)...............(1) y=a(1-cosθ) .............(2)

Q: et sin t? blas Y - et cos t? lio -n/2 <t < 0

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Q: Suppose A(t) = [ e^t 0 0 0 cos t sin t 0 −sin t cos t]…

A: Given: At=et000cos tsin t0-sin tcos t To Find: To show that At-1 exists and then to find it.

Q: Let y(x) be the solution for the DE. y+y tan(x) + sin(x) = 0 If y(0) = In 2, then at x = %3D %3D the…

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Q: Let C be the curve parameterized by Y: [0, b] R³, y(s) = (12 cos(s²), 12 sin(s), 9 s²). Find b>0…

A: The given problem is to find the value of b for which the given length of curve of the given…

Q: Suppose r(t) = cos(nt) i + sin(at) j + 5tk represents the position of a particle on a helix, where z…

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Q: If z=x+iy=r(cos(6) + isin(0)) then arc z=0 %3D |z|=/x² +y² =rO %3D

A: The correct option is 4th option. i.e.Z=x2+y2=r i.e. if Z=x+iy=r(cos(θ)+isin(θ)) then Z=x2+y2=r .

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 3…

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Q: 1) If dy = tan x, then y =? dx А. !tan?x + C B. sec?x + C C. In [sec x]+ C D. Inſcos x] + C 2) dx =?…

A: We have to choose the correct option.

Q: Ary sin(r'y) +r + [x? sin(x²y) + 2y]y = 0

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Q: Given f(x,y) = eX cos y, Evaluate fy(2,0) O cos 2 O sin 2

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Q: Find the exact length of the curve. y = In(cos(x)), TC 0 < x<.

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Q: What is the general solution of (2ry – tan y) dx + (x² – rsecy) dy = 0 ? %3D atany 222y 12 sec2 y =…

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Q: - Find the aera under the curve y = cosx Form x = 0 to x = -fx sec² (ax² )dx a#0

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Q: f(x, y) =- sin xcos y, then

A: The given function is: f(x,y)=-sin xcos y To find ∂2f∂x2. Here, note that y is constant w.r.t. x.

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

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Q: Find the aera under the curve y = cosx fx sec²(ax² )dx a #0 Form x = 0 to x = 7/

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Q: Sketch the regions enclosed by the given curves y-4 cos(7x), y- 4 sin(14x), x -D, x-/14 0.05 0.10…

A: The solution of above question is written below.

Q: 50. w = sin x + y²z + 2z, arcsin(t – 1), y = t³, z = 3 %3D

A: Since you have posted multiple question in this question which are not interlinked so I have solved…

Q: Given: z = cos(xy) dz Find: ду dz ду dz - tan(xy) = -x sin(xy) ду dz = tan(xy) = -y sin(xy) ||

A: Given: z=cos (xy)Find: ∂z∂y=?

Q: x²+y²` du du =+y dx If u=sin| ,x+y #0,Prove that x =tan u x+y dy

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Q: The length of the curve y = In(cos x), 0< x <:

A: To determine the length of the curve, y=lncos x, 0≤x≤π4.

Q: A rod with density p(x)=4+sin(x) (in grams per cm) lies on the x-axis between x=0 and x=pi/3. Find…

A: Please see the explanation below

Q: 2" + y = cos a, y" - z = sin r, z(0) = 1, 2'(0) = -1, y(0) = 1, y'(0) = 0.

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Q: 3) Find the exact length of the curve. y = In(cos r), 0 < x<

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Q: Find the length of one arch of the cycloid x= 6(t-sin(t)) y= 6(1-cos(t))

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