4. y = c, sin wt + c, cos wt w is a parameter

Q: dz dt Consider x = cos t, y = sint and z = x2 +y². Then ulan ||

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Q: Can you help me step by step?

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Q: 9. If y = sinh 4t and r = sinh t, show that 2 dy (a) (1+2²) = 16(y? +1), dr dy (b) (1+x²)- dx2 dy…

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Q: 22) sin(y)dx+cos(y)dy = 0

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Q: If y = atan (0) „x =a sec (0) prove or disprove d'y 3 cot(0) 4a dx

A: y =a tan3θ   ,   x = a sec2θ     'y' is a function of 'θ' and 'x' is also      a function of…

Q: Given z = 2 cos t + 33 and y = 8 sin²t dz (i) dt dy (ii) dt dy (iii) dr

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Q: 4. Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t² , (0 <t< 1).

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Q: 4. y" + y = tan x. 5. 4y" – 4y' – 8y = 8e-t 6. y" – 2y + y = : + 3e 1+ t2 et 7. 4y" +y = cos I

A: 4. Given, y"+y=tanx

Q: 16. t 31²y = cos t, y(T) = 0 dt

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Q: If z = cos x - e¹, x = 1² + 1 and y = 5 + ln t, then equals: dz dt

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Q: (4) Evaluate sin(yz)dr+xz cos(yz)dy+ry cos(yz)dz, where C is any curve joining the point (0, 0,0) to…

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Q: (x,() + x(x, t) = sin(t) u(n, 0) = cos(7), at %3D %3D nER.

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Q: If y(u) = Cos v -dv then y'(u) =

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Q: If y In(z- y) then y at the point where y = 0 is equal to

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Q: S S§y²cos(xy)dydx

A: we have given,                 ∫x =0x=1∫y=0y=π4y2cos(xy)dydx After arrangement,…

Q: Q1: If Z = x³ + y* + (x sin y) + (y cos x), Find Zx/Zy?

A: We are given: Z=x3+y4+(x sin y)+(y cos x)To find: ZxZy This can be calculated as follows:

Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, 4t2), o sts 1. (Round your answer to…

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Q: 1 ezt dz 2ni Izl=2 z2+1 cos (t) o tan (t) o sec (t) o sin(t) o

A: See the attachment

Q: 11. dw 12. J(Gu - 1)(3u* + 2) du J-scos z + 4 sec" x) dx 13.

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Q: SORU 7) S*-[(sint)i + (1+ cos t)i + (sec? t)k] dt =?

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Q: 1) (22 - ry + y?)dx - xydy 0, where y(1) = 0

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Q: }} If y cos(xy) dydx = x=0 y=0

A: Here we have to find the integral.

Q: Find the area between the two curves.

A: The area between the curves y=sec2x and y=sin2x on interval 0, π4:The area between curves is the…

Q: Evaluate [y cos (3y) dy

A: We use integration by parts continuously. ∫f(y)g(y)dy =f(y)∫g(y)dy  - ∫df(y)dy(∫g(y)dy )dy Also note…

Q: -If x= cot- VE, y = ;, find dy dx'dx2 at t = 2.

A: We will use the formula (f(g(x))' = f'(g(x))g'(x)uv' = vu'-uv'v2 Given x = cot-1ty = 1t+1 Then dxdt…

Q: Solve the DE Ssinx siny dx + cosx cosy dy = 0 by separation of variables. sin y A cos X B sinx cosy…

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Q: Find if y%3D cos (2x)+ 2еж: dx dy

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Q: 3) Find if w = 5 cos(xy) – sin(xy), x = ,y = t,z = t³ %3D dt

A: Let's find.

Q: 7. Calculate dy/dx at the point indicated: f(0) = (7tan O, cos O), 0=/4

A: Here we will use the concept of parametric equation and Derivative of parametric ewyations

Q: 21 Find Ez hox) Cx siny +y cosy)it hex cxcosy-ysiny) 5 aanon Ze o Pn hex) for which conserrabive on…

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Q: (1 + cos 2y) dr - 2r dy = 0, y(1) = i %3D Oy = Arctan 2 O y = Arctan O y = Arctan ( 1) D y = Arctan…

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Q: dz az B. Find əx and ay 3. x eY+ cos xy36xz+5x²

A: partial derivative

Q: dW Find at t=0, if dt .3, W = x*y+ zxy whe x = sin2t, y = cos ?

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Q: 3. If x = (sin t+cos t), y = (cos t-sin t), (1 < t < 4), evaluate ip, dt. dt dt

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Q: 25) 2 sin(y)dx+cos(y)dy 0, y(0) = z/2

A: Q 23 is incomplete as it doesnot contain dy term. and Q 25 is in next step.

Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, t2), 0 sts 1. (Round your answer to…

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Q: 3. Find dy/dx of the followings: (а) у | V2 + cos³ t dt 2. •7x2 (Ъ) у V2 + cos³ t dt 2 (c) Y 1 dt t2…

A: using fundamental theorem of calculus part 1 ddx(∫abf(t)dt)=f(b)ddx(b)-f(a)ddx(a)

Q: 1. Find fx,fy,andfz f(x,y,z)=sin(xy)cos(yz2)

A: It os partial derivative wrt x y z

Q: dw 3) Find ifw = 5 cos(xy) – sin(xy),x = ,y = t,z = t³ - %3D dt

A: Given: w=5cosxy-sinxy, x=1t, y=t, z=t3 For finding dwdt, first we find w in terms of t So, we put…

Q: Ex: verifay u = e* cos y is a solution of laplace eqution

A: Solution:Given             u=ex cos yTo verify u is a solution of Laplace equation:i.e.,…

Q: 3) I Cos dydx Ins Iny 4) S S e** dxdy X 1 0

A: 3)  Given:      ∫π2π∫0x21xcosyxdydx       =∫π2π∫0x21xcosyxdydx

Q: Solve the initiol volwe problem using Laploce tronsformotion, y - e"sint y (4) + 2y' (+) +5y(+) y…

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Q: * sin(Iny)dy is equal to y A -cos(ny) + C B none of these cos(Iny) + C y D cos((ny) + C cos(Iny) + C…

A: A standard integral in some cases can be converted to a standard integral with an appropriate…

Q: (у — сos-x)dx + cos x dy %3D 0

A: The given equation is y-cos2xdx+cosx dy=0 rewrite it as y-cos2x+cosx…

Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

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Q: 2²y ds, C:x = cos t, y = sin t, z = t, 0 < t < a/2

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Q: 40. (e' sin y+ tan y) dx + (e' cos y + x sec? y) dy = 0

A: