2. Show that 4=x i+y°j+:'k is irotational.

Q: | cos zdr + sen ydy + x?dz

A: The solution are next step

Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: Q7 Show that CX,y) =e is Condinuous at co,0)

A: The given function is:  fx,y=e-x2+y2 The given point is 0,0

Q: Given, x(t) -t+3 Draw the 3 s7+ 7è + 7 = (7) A figuezes f (xy4) = In (xy) + x siny / figurees…

A: Solution is given below:

Q: If y = cos ¹ prove Zyy + z = 0. )Z = (1 + i)(2-1)-¹, find |Z|.

A: Here given y=cos-1(z/x). We prove that zyy+z=0.

Q: ! = 0.25y² is to (implicit) Euler's condition y = 1 at What would be th

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Q: O(y-+ rycota)dr + zdy O (coszcosy– cotz)dr sinrsinydy 0 O ydr + (3z -g')dy = 0

A: A differential equation is called linear if 1) every dependent variable and derivative involved…

Q: If u(t) = (sin(2t), cos(2t), t) and v(t) = (t, cos(2t), sin(2t)), use Formula 5 of this theorem to…

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Q: and casy=0t, and DLyr, Furd the exact alue of tan Ca-y.

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Q: - If x=sect and y = tan t, evaluate at t of the following: 4. dy (a) dx d y (b) dx?

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Q: 1. If H(y) = cos y – sin y, Find H (0), H (),H (1T), and also show that %3D + x) = H (T – x) = -H…

A: Given that H(y)=cosy-siny find H(0), Hπ2, Hπ Show that  Hπ2+x=Hπ-x=-H-x

Q: Reduce the given DE into Bernoulli's equation: dy_y 2x* y-4 - dx 3.

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Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

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Q: Find he value of ds /dy at u = 2 if s = t2 + 5t and t (u² + 2u)3 du %3D

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Q: 9/ Evalaale he fillow inlag rad S sin'z asx dy x CoSx

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = || N, = X, Since M,…

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Q: 1 Suppose z = In(6q) and q = Vu +4 tan¬(3u). Find dz/ðu and dz/dv when u = ÷, v = -3. 3

A: Given data: The first function is z=ln(6q). The second function is q=√(v+4)tan-1(3u). The value of…

Q: 6. If w=xy + yz + zx. x =r cos0, y = r sin0, z= r0, Find dw/dr, dw/dO, when r = 2,0 =x / 2.

A: Answer

Q: 8:54 1 3. If y = (5x)sin(3x) , then %3D dy %3D dx Type here to search

A: This question is related to differentiations. Solve in 2nd step.

Q: Find the value of ds/du at u = 2 if s = t^2 + 5t and t = (u2 + 2u)^(1/3).

A: Find ds/dt from s=t^2+5t

Q: O Consider d = - CoSk; yeo) =0,iylo) Reduce he abore initial vaeue problem To be roltera entegral…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Verify that the indicătéd function is an exp for each solution. y" - 6y' + 25y = 0; y = e3x cos 4x…

A: Recall: (uv)'=u'v+uv' where u and v are the function of x

Q: Without eliminating the parameter, find d²y at t = 2 1 x = 1

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Q: If r(t) = (V10 – t, In(t – 1), sin(2t)) , then the domain of r is

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Q: If u = sin® 3 - x 2 find Ou Əx Ou and ह Hence show that 2 Ou 1 y x 3 –x dy Ou = 0

A: Given u=sin-13-xy2

Q: 3) if y= CoSX then shift it by a) left TC b) Down1, lett 2

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Q: Given z = 15 In(t) and y =225 t then find dy da dy da?

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

A: differentiate with respect to x

Q: 21. ds: C is the quarter-circle r(t) = (2 cos t, 2 sin t), for 0SIST/2.

A:

Q: 2. (a) Determine c, and cz that y = c¿e³x + c2e¯2x + 2 sin x will satisfy the conditions y(0) = 0…

A: We have to determined the value of C1 and C2that y=C1e3x+C2e-2x+2sinx will satisfy the condition…

Q: Q6A)If y = cos ¹) prove Zyy + z = 0.

A: See this solution in below

Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, 15

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Find the par ticular solution of the differencial 4. given x=0 and y= eguation dy -20cH1) (x+1)

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Q: From a sketch of the direction field, what can one say about the behavior as x approaches +o of a…

A: dydx=3-y+1xTo Find: From a sketch of the directional field state the behavior as x approaches +∞ of…

Q: Q:Ifx= sin 6, y = 0,y = cos pe, prove that (1-x )y,-xy,+p°y = 0, %3D dy where y, dy and y1 d

A: Here given that x=sinθ, y=cospθ Taking derivative of both x & y with respect to θ, we get…

Q: 7. Find fSp(x - y)*dx dy, where D is Figure 17.2.13. y A シ=V ソ=2-

A: Answer is 64/35

Q: s zy dydz こミ0

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Q: 3. (1+ 2y²)y' = y.cos (x) diferansiyel denkleminin türü nedir?

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Q: Show that the tollawiny ey uation has a solution 9(4) 5.t lim y 4)=9 そ-3 I y't (cos?t) y't (sin t) y…

A: Given equation is y''+cos2ty'+sinty=0 It is a homogeneous differential equation of second order. The…

Q: (b) If u = x² cos y+ye", where x = s+2t and y = st, prove that ди ди 2 = (s – 2t) (x siny– xye –…

A: u=x2cosy+yexyx=s+2ty=st

Q: Given z 15 In(t) and y= 225 t then find dy da dy dr?

A: Given that: x=15ln ty=225 t2

Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

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

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Q: (5) Under what Conditions is (ax+by) dx + (KX+LY)dy=o exact? selve the eXact equation,Ca, b,k, L…

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Q: 1 Sa dy secy tany S sin ²x cos²x dx 2. S

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Q: 6. If x= sect and y=tant, evaluate at t =- of the following: dy (a) dx d'y (b) dx?

A: x = sect y = tant

Q: 11 z- CCW -dz, z2 - z de. c:|2- = sec(u), <ý<.cv Question 11) Find I =

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Q: If r(t) = (VE – 1, ln(10 – t), sin(2t)) then the domain of r is

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