dy in terms of y? dx %3D - 12. Given that 3x – tan y = 4, what is dy (A) = 3 sin" y %3D dx dy 3 cos? y (B) dx %3D dy (C) = 3 cos ycot y dx dy (D) dx 3 1 + 9y2 II

Q: Given arccot(sin(2x + y)) + arctan(cos(2x + y)) = 0, solve for dx %3D dy

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Q: d²y If y=cos 4xr, then at x = 0 dx?

A: Given,     y=cos4x

Q: d²y Find С. dx? 1. y= sin 2x +cos² x sin x 2. у- - y= 1-cosx

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Q: dy 3. dx y – x + cos - -

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Q: Find dy/dx and d2y/dx2. x = 8? + cos ?,    y = 9? − sin ?

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Q: dy 7. dx cos(x + y), when x = 0,y = 4

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Q: dy dy +у сos x + 2xey — Зх2 %3D (1 — х?ey) dx sin x dx

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Q: dy given that In(x + y2)-tan-1 31) Find = 0. dx

A: Given: lnx2+y2-tan-1yx=0 To Find: dydx=?

Q: dy If x=5+ cos20 and y=3- sin20 , what is dx

A: We have to solve the problem

Q: dy dy implicitly in terms of x and y. Hence, find d.x Given sin(xy) + 3e 3y?. Find dx when x = 0 and…

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Q: Use this equation to find dy/dx. 5y cos(x) = x2 + y2 %3D dy dx %3D

A: We have, Here, we'll take derivative on both side and then isolate the dy/dx.   It is known that,

Q: Find dy/dx for the fo d) x' + x.tan y = y -1

A: There are multiple question, As per our company policy ask other question separately. d.

Q: dy given that In(x + y2)-tan- = 0. Find dx

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Q: D- y" + 2y' + 5y = 6e2* + x sin? x + e*cos 2x %3D

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Q: dy d'y dx ' dx? 2. If y = sin 2x – 2 cos 3x,the find, at x 0

A: The given function isy=sin2x-2cos3xto finddydx, d2ydx2    at x=0

Q: PCx g) - Sin (zy)- Cosx'+x*y? %3D find d'f df dye' de dy

A: Given function is  f(x,y) = sin(x,y) - cosx^2 + x^2y^2

Q: The dy/dx for y=-4x+7 cos x d/dx (-4x+7 cos x )=

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Q: dy Vi-y 2. dx 1. tan y dy Ans. x cos y = C Ans. sin 'y = sin 'x + C dx Ji.

A: Variable separable form of differential equation: Let us consider differential equation of the form:…

Q: e2 (2 cos y dx – sin y dy) = 0, y(0) = 0 – sin y dy) = 0, У (0) %3D

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Q: 4 Find dy/dx for: y = sec?x- tan²x b- y = sec -x) C- y = sin(tan(3x))

A: It is asked to differentiate the following functions with respect to x: a) y=sec2x-tan2x b)…

Q: dy cos?x = -(tan x)y ;y(0) = -1 b) Solve %3D dx

A: Given that: dydx-cos2x=-(tanx)y; y(0)=-1

Q: dy Find dx -1(In 8x*) y= tan %3D dy %3D dx

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Q: (y? cos x – 3x?y – 2x) dx + (2y sin x- x'+ In y) dy = o

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Q: dy Find dx 1-4x V1+4x (a) y= cos'(sinx) (b) y = = arctan

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Q: cos(x + y), when x = 0,y = dx 2 = dy : %3D

A: To solve the differential equation we can use a substitution u=x+y and then we can use variable…

Q: d*y _2d'y dx d²y_gdy +4y = 0. dx dx dx Ans.: y= (C, +C,x)e* +C, cos 2.x + C, sin2x.

A: Given the homogeneous linear differential equation with constant coefficient is…

Q: dy, ycosx+ sin y + y_ o Solve dx %3D sin x + x cos y + x

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Q: y²dy e2x а. dx У (0) %3D 1 ex b. 8 cos? y dx + csc² x dy = 0, %3D y 12 4

A: Part(a) We have  y2dydx=e2x+1ex, with initial condition y0=1 This can be written as: y2dy=e2x+1exdx

Q: dy -y In (yecos)dx 4. COS Y sin x dx

A: The detailed solution is given below Thank you

Q: z=cos y Using the substitutions the DE (3cos y – 5x)dx – 2x?tan y dy =0 reduces to dz = - sin y dy A…

A: Using given substitution.

Q: dy Find xp. y = tan -1( In 2x°) %3D dy xp

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Q: * = cos(x + y), when x = 0,y = = %3D dx

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Q: dy I. y = cos(2t), x = sint = =? dx %3D

A: As per our guidelines we are allowed to solve one question at a time . kindly repost the rest…

Q: + yž = 1, when x = 0, y = 4 dx cos(x + y), when x = 0,y =" dx

A: The objective is to find the solution of the differential equation.

Q: 5. dy/dx + (y/x ) = ( y/x )? 6. x² dy/dx -y² = 0 du u YCot x dx = tan? x dx ; y = 2 when x = %3D 4.

A: Solve above differential equations.

Q: Find the solution where y= 1 and dy/dx = 0 when x =0 and describe the behaviour of the solution for…

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Q: a) arctan(y) dx + 1+y2' dy = 0 b) (x² + y²)dx + (2xy+ cosy)dy = 0 %3D

A: Here we have to check whether the above ODE is an exact DE and if they do exist then we have to…

Q: dy If x = 3 sin t and y = 2 cos"t, then find at /= dx Oa0.76 Ob.0.86 OC 0.67 Od.0.56

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Q: Find dy dx 12) y = cos ³ (5x+2) -2)) y = √tan √√₂x + + 3)) Por The following Function i y = sin-¹…

A: **As per our guidelines, we are supposed to answer only 3 subparts of a question. Since you have…

Q: 20.1 please provide all necessary solutions and explanations.

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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: . (бх + у?)dx + у(2х — Зу)dy %3D 0 . (2ху — tan y) dx + (x? — xsec'y)dy -о

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Q: dy Find for the following fur dx 2- COS X y% = 7+ coS X dx

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Q: dx 3. 2y cos x + 4y sin x = sin 2x, given y =0 when x n/3.

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Q: dy 7. dx = cos(x + y), when x = 0,y == 4

A: Differential equations, with substitution method and separation of variables

Q: dy No need to simplify. А. Find dx 1. y = cos 3x 2. y = tan? | 3x² 3. y = 5x$ 13

A: We know that  ddxcosax+b= -sinax+bddxax+b ddxtan fx = sec2fxddxfx and ddxxn=nxn-1

Q: dy dx 2. 2X for y = cos (Inx + e) %3D

A: ddx(Cos(x)) = -sin(x)ddxex =exddx(log(x)) =1xddxxn=nxn-1Chain ruleddxf(f(x)) =f'(f'(x)) Here , In…