If y(u) J5 COs v9 dv then cos(9u eIu y'(u) = %3D e4

Q: (a) | (2x cos y + sin x) dx 6. */2 (b) I| (2xcosy+ sin x) dx dy

A: Solving integral

Q: 3. cos y sin 2x dx + (cos² y – cos² x)dy = 0

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Q: (3e* sin(y) + y)dx + (2x + e* cos(y))dy = 0 not exact

A: Que is not clear though. We Shall check exactness for the given differential equation. If you have…

Q: cos² (6y) + sin²(6y) = y + 12.

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Q: Q3) Find dy/dx if 1- y= In x 2- y=x sinx+1-x

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Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

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Q: If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] True or False.

A: Given statement If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] is false.

Q: Find dz/dx and dz/dy for: x² sin (y³) + xe32 – cos(z²) = 3y – 6z + 8

A: Here, the given equation is: x2sin(y3)+xe3z-cos(z2)=3y-6z+8...(1) So, z is a function of x and y

Q: Find dy/dx at x=0 if y= Cosu and y--3x

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Q: If y=(sin3x-cos3x)², find dy dx

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Q: cos 2x dx (b) 4 cos t dt 0 2

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: dy dx if y=Vsinx +sin Vx+ cos(2x)

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Q: 3y dx 2 (2y In +3 sin y]dy =- + 3 Sin Y X+ 3

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Q: Compute dy/dx if sin(x) = cos(xy^2

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Q: b. sin 2xdy – 2(y - cosx)dx = 0; when x = 1/4, y = 0

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Q: dy tan tan x = 0 dx coscos x +

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Q: 11) (3ycos(3x)dx– sin(3x)dy)/ y = 0 12) sin(ß y)dx =-ß cos(B y)dy

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Q: 15 dy dt 2-

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Q: dy/dx of y = (x^2)cos^4(x)

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Q: | cos 3y dy 4.

A: I=∫ cos6(3y) dy3y=tdy=t3Integration by parts;∫uv dx=u∫v dx -∫ dudx ∫vdx dxI=13 ∫ cos6t…

Q: What is the integrating factor of (y – cos² x) dx + cos xdy = 0?

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Q: 1) ſ y³ sin(2y) dy

A: As per our guidelines we are supposed to answer one question , kindly repost the remaining questions…

Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

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Q: arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B)…

A: ∫arctan(ekx)1+e2kxdxFormula to be used :1.Intergration  by parts2.Substitution3.ddxarctan(ekx) =…

Q: Find dy/dx if y= cos-1 In(x+1)

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Q: Ssin (2x)cos(2r)dx

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Q: find dy/dx if y = (sin-1 x)2

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Q: dy 1- cosh x + (sinh x)y = e¯x dx 2 dy 2- - y = e*/2y³ dx

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Q: find dy/dx if(cosx)y=(siny)x

A: Given: -

Q: (3+y +2y² sin2x) dx + ex + 2xy -y rin 2x) dy=O

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Q: 2- Find of y = dy dx y %3D /cos-1(In (xy))

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Q: 2sin(y)cos(y) sint(y)+costy) dy

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Q: ( cos nx dx= [cos %3D nx cos nx dx 0. %D

A: We have to find the integral of cos2nx dx from 0 to 2pi.

Q: -5 1 -dx Jo 2x+4 1 dt 2 V6-t 1 ii) S,

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Q: Whatis the derivative of y = sin (2x − 1)? dx = 2 cos (2x - 1) dy dx = cos 2x dy -2 cos (2x - 1) cos…

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Q: - sin y, dz = cos x dx – cos y dy

A: Consider the given differential equation as, dydx=sinx-y

Q: if  x²v+sin(xu)-yv²+u³v=1 x²u-2yv=1 ، cos(xu)+yv=5  ,find dy/dx

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Q: 2n Sin (3y) dx + 3x Cos(ay) dly =o

A: Given differential equation is 2xsin(3y)dx+3x2cos(3y)dy=0

Q: ion dy 3t2 dt 2y + 2t3y' tion: ||

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Q: 4. cos x dy + y(sin x – 1)dx = 0; when x = T, y = -2

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Q: dy of y = sin(3x² + 5x – 4) * In(e*) is dx

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Q: y=sin-1x

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Q: 25. (2y cosx + sint x)dx sin x dy , when x =y = 1 %3D %3D

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Q: dx o ex+x е. f. S sin(vE) dt S dx 2x cos(vE) dt COS g. dx 'x

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Q: dy/dx at the same point (1,0) is

A: Given: The equation is y = ln ( x2 + y2 ) and the point (1 , 0).

Q: 3) [ - cos dydx X X In 8 In y 4) S S e**y dxdy

A: (3) we have to evaluate ∫π2π∫0x21xcosyxdydx let  u =yx ⇒dudy=ddyyx         =1xddyy=1x⇒du = 1xdy…

Q: (2e" sin(y) – 4y)dr + (–7x - e cos(3)dy = 0 not exact

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Q: 5) ( cos 'x dx -1 Where: u = cos(x) dv = dx

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Q: If y = (4x² – 3x+ 2)(e2* – cos 3x), then find dy at x = 0. dx -2x %3D - -

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