If X =r cose equation (d ,y=r sin@ then show that the will be Erans formed into dy 2. 3D0 dr

Q: Obtain the general solution por the di fferential equation %3D .(yd -x² )dy= 2xy dx %3D

A: Given; 1) y'=(x-y)/y. 2) (y2-x2)dy=2xydx.

Q: 2 X(+) = SIN'セ y (t) = Cos?t 9) IF dy FIND %3D

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Q: sec-(2y cos r) = x"

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Q: Given that cos(2x+y）=4xsiny, where 0≤y≤π, find the value of y and dy/dx when x=0

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Q: dy sin(x) Find for y = dr -3

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Q: [(VxA)• dS over the surface of a hemispherical b 2 and its circular rim if A = 3 sin()â

A: Sol

Q: QUESTION 4 If y = (sinx), show that %3D (1 – 2) dy dy 2. dr? dr

A: Explanation of the answer is as follows

Q: The equation + dx y = xy can be classified as FOLDE and Bernoulli’s equation. A True False

A: True.

Q: 4. y = csc x sin x + (sec? x + tan²x)

A: I have stated the used formulas in the solution

Q: d'y Find for dr? y = cot(x) dy %3D dx?

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Q: (x** ye) dx + zy dy

A: To Solve for the general solution of the following first order differential equations.

Q: Find the values of a and b that make following D. E is exact (-) dx + (xy + 1) dy =

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Q: d) y = sin*(x'/3) + arctan(r?)

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Q: 3. y = tan(sin 2x)

A: Please see the answer below.

Q: The equation Can be using the mne thod of Separation of Varia bles dy Sin(x+y) |3D And the output is…

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Q: 1. Given that Y = e + Cosx, find: dy a. dr b. d'y/dx?

A: Hello , thanks for your question but according to our policy I am answering the very first question…

Q: dz az Find and of the equation z = xy arctan ax ду

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Q: Given [2r + y cos(ry)] dx +r cos(ry)dy 0. Show that the equation is exact and find its solution.

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Q: Express the circular function cos+sin as a single cosine with a phase displacement T Rcos (+a) where…

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Q: dy Solve the equation sin (r) with initial condition y(0) = –1 using Separation of Variables. %3D da

A: Consider the equation: dydx=sin2xy,    y0=-1 To solve the given equation,…

Q: Question 6 af Given f = esec (#) -ya+y, find dy (#) sec² (=) ye NO -y+In (y)

A: Given :f=esecxy-yx+y

Q: 5. y = sin* x + cos* x

A: y= sin4x + cos4xdifferentiating w.r.t. x;dydx=ddx(sin4x) +ddx(cos4x)     =4 sin4-1x ddx(sinx)…

Q: If we solve the DE y dx + 2 x dy 0 alter converting it to Exad using an

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Q: 6 3 oy sin (a? + 3²) dædy Find

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Q: Find dy/dx in the following: -1 2. Y= cos cot x

A: The given function is: y=cos-1cotx           From the property of inverse trigonometric function, we…

Q: dx + 2xy = sin y , x(n) = 1 - dy

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Q: Given x = sin3t, y = -cos3t, then find at t =. %3D dx а. 1 b. 3 с. О d. 2

A: We need to find dy/dx.

Q: 5. J sin42x cos22x dx.

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

Q: If y = (tane) /28 +1 find dy then choose the correct answer: %3D dx

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Q: 8. y = Jcos x – 4 sin(1 + x3

A: To give what is asked. To find dydx. To show the solution. y=cos x-4 sin1+x13

Q: the Yp Vvnich OllOWing is a particu y" + 2y' + 5y = sin t where A; are constants determined by…

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Q: -x2 + 5 2. y = cos 2x³

A: Given: y=-x2+5cos2x3

Q: Find dw/dx, dw/dy, and dw/dz. 47. w = ye sin xz %3D

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Q: Which of the following equations is NOT an exact equation? (2x sin y + y)dx + (x² cos y + x)dy = 0…

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Q: If y = (sin¬1 x)², show that dy (1 – x²) da? dy = 2. dr

A: y=(sin-1x)2 we have to show  (1-x2)d2ydx2-xdydx=2

Q: QUESTION 5 dy If y=5sinu and u=4e%, then the value of Y dx 4cos(5x) cos(20x) • 20cos(4eX) 20cos(5eX)

A: To find this will use chain rule of differentiation If y = f(u) and u= g(x) then according to chain…

Q: I d²u dv² tan v sec“ V

A: Find your answer below

Q: If zy + sin y + arctan(z) = then what is the value of at (1,0)? a)-1 b) 1 C) 0 d) -2 e) 2

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Q: If y = cosx, then dy dx is

A: Given that y = cosx  And we find its first derivative with respect to x. And after we put the value…

Q: dy 1- Sinx+ Cos2y3D0 dx

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

Q: If y= cose* then dy dx 11

A: Solve the given

Q: if y= In(arctan (2 x)), dy=? XP

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Q: Let y = 78 cos -e. Find dy using any method. Express your answer in dx %3D terms of x only. dy %3D…

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Q: NOTE: Enter the exact answer. yz dx dz dy = %3D -90

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Q: Question 12 of 12 fe #0. dz and ye-8 sin 4z = 4z %3D dz dx dz dy II

A: The objective is to find the partial derivatives.

Q: Given I = 4 In(t) and y= 16 t then find dy dx dy da?

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Q: Find the Product solutions of 2) du du - I dy dx +

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Q: The position of a particle in the xy-plane at time t is given by r(t) = (cos 2t) i+ (2 sin 2t) j…

A: Given: rt=cos2ti+2sin2tj For finding equation in x and y whose graph is the path of the particle, we…

Q: Given a = 2 cost + 20 and y = 5 sin?t de (6) dt dy (é) dy (é) de ||

A: We have to find the derivative of given functions