z = uv + v2, u = tan- x, v= y(x² + 1) Find zxy

Q: find the integrating factor of cos(x)y'+sin (x)y=2cos^3(x)sin(x)-1

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Q: 9 y = Arctan(2+x 1-2x 10. x = cos't ; y = sin't

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Q: y sin(Vu +3u-1) Oy = Vx x+ vZx y = e* sec(tan(x*)) y%3D u = In cos(x? + 1)|

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Q: (2y cosx + sin“ x)dx = sin x dy ,when x =",y = 1 5y= 1 %3D X 2

A: 2ycosx+sin4xdx=sinxdy,   x=π2,   y=1:A first order linear ODE has the form of y'x+pxy=qxLet y be the…

Q: * (D'+1)y(x) = tan(x) 1-sin(x) 1+sin(x) 1+cos(x) - y,(x) = sin(x)In m(x)s03 = (x) 2- -- y,(x) =…

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Q: find ƒx , ƒy  . 1. ƒ(x, y) = ln (x + y) 2. ƒ(x, y) = sin^2 (x - 3y)

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Q: y In x – x In y = 4, y' y In (x² + y² )= 2 arctan 2) = 2 arctan y'

A: This question can be solved using the concept of differentiation of implicit function.

Q: sen z + cos x dz | (tag z + 1) dx = In sec x+z + C 37. %3D cos 2

A: 37.   Given integral, ∫sen x+ cos xcos xdx

Q: y" + y = sec x tan x

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Q: 7. Differentiate w.r.t x- sin 5x cos 3x 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

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Q: 4) S(x, y) = (4x-x* )cos(y) on the Ans. Absolute max.: 4 at(2,0) 3/2 Absolute min.: at 2 rectangular…

A: Given

Q: 3. S sec z tan z dz 2 2

A: Given: 3.∫sec23z tan23zdz

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = tanh (x + 2y + 3z)

A: We have given fx,y,z=tanhx+2y+3z and we have to calculate fx,fy and fz

Q: tan x + i tanh y 1- i tan x tanh y 18. tan z = tan(x + iy)

A: We have to prove

Q: (ysin x+xy cos x)dx+(xsin x+1)dy = 0 Ans. xy sin x+ y = c

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Q: 1. If tan-1 x x 1’ f(x) = Then S(x) dx =?

A: This question is related to definite integration, We will solve it using given information.

Q: RFind dy/dx in terms of x and y if cos²(8y) + sin²(8y) = y+4. |

A: Given query is to find the derivative of the given expression. Pp

Q: 3. [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]³dx gettyimages FUsC When:x = 0; y…

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Q: sin x dy Given: y = Compute for dx 1-2 cos x

A: The given function is y=sin x1-2 cos x

Q: 2. (y² cos x – sin x)dx + (2y sin x + 2)dy = 0 (Exact)

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Q: (. 0) S(x, y) = In(x² + xy), at (4, 1) S(x, y) = sin (x²) + cos y, at

A: 19. f(x, y)=sin(x2)+cos y At π2, 0, fπ2, 0=sinπ22+cos 0                =sinπ4+cos 0…

Q: 1. If z=ln (x-y) +tan (x+y) find zxx and zyy

A: Given: z=lnx-y+tanx+y  ……1

Q: tan y-1 . sin y- cos y- 1 www. Prove that tan y +1 sin y + cos y+1 2.

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sec-1 (x + yz)

A: Given that f(x, y, z)=sec-1(x+yz)

Q: Ssin x x cos x dx = %3D Select one: а. -cos 2x +C 4 b. -cos x + C 4 c. -sin 2x + C 4 d. -sin x + C 4

A: We need to evaluate the following integral ∫sinxcosxdx

Q: y = tan In(x + sin x) %3D y = sin x + In sin e* %3D

A: y=tan ln(x+sinx) y=sinx+ln sinex

Q: (4,0,2) S sin y cos x dx + cos y sin x dy + 3 dz (1,0,0)

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Q: d sec z = sec z tan z dz

A: The function is a rule that associates or fixes a number to the particular point z . If , then the…

Q: y = Vr² + VT etin e y = r-5 y = (cos z)n. y = /tan 2x – sec3 (4x – 1)

A: as we are just given 4 functions and not any question so I assume we need to find the derivative of…

Q: Find the general solution for (cosx)y' = 1 – y² consider y, (x) = sinx. %3D

A: Given:  cosxy'=1-y2                  1          , y1x=sinx Let y=y1+u be a solution of (1)…

Q: (2y cosx + sin* x)dx sin x dy, when x = y = =,y= 1

A: Given - 2ycosx + sin3xdx = sinx dy , when x = π2, y = 1 To find - Solve the following differential…

Q: 3. [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]*dx gettyimages When:x= 0;y =, %3D

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Q: 4. z(w) = –13 sin(w) + 11 tan(w) – 5 sec(w) 5. b(y) = 4 ln(y) + 2"

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Q: tanx If f(x) = (Α) B C D S 0 sec ³x 1+etanx In (secx) √ 1+tan²x tanx 1+e sec²x 1+ etanx 1+1² -dt,…

A: Here, given that: f(x)=∫0tan x1+t21+etdt...(1)

Q: Find if y sin x = x³+ cos y %3D dx 312- -COS I sin z-sin y O 3x +y cos I sin r+sin y O 3z+y cos r…

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Q: tan" -1 I# Z-X FEMD fyx At (-,1).

A: The solution for the above question is as shown below.

Q: 1 -dx= cosº x/2sinx 5 /tanx+=Vtanº x + C А. Vtanx+/tan5x+C 1 B. tanx +÷Vtan° x +C С. 2 2 tan x +C 1…

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Q: i. y = x-% % -4Vx ii. y = x+Inx+ sin(3x) iii. y = x° cOS X y = x° cos x

A: Use product rule of differentiation

Q: (xSin 受)x x cas dy -y Cos X Cos

A: Thr solution is given in the next step.

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: d tan(2) = %3D dz sec(x) O cot(x) O sec-(z) O sec (z) tan (z) O

A: We use the standard results of derivatives.

Q: cos(0)x – sin(0)y] sin(0)x + cos(0)Y T z || నా

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Q: (8 cos x cos y + 4 sin x sin 2y + 1) dx – 8(sin x sin y + cos x cos 2 2y) dy = 0

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Q: [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]³ dx gettyimages When:x= 0; y = 2

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Q: sin x dy (1 + y) cos x + sin x If y=- , prove dx %3| cos x 1+2y + cos x- sin x 1+ sin x 1+ 1+ coS x…

A: Introduction :

Q: 3. sin y(x+sin y)dx + 2x² cos ydy = 0 0: uhen v-2

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Q: 2. Integrate: a) Sx cos(x²) dx g) [3 cos(2nx) dx b) S tan³ x sec²x dx h) Se2% sin(e²*) dx c) S cot x…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Test for homogeneity

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Q: Obtain a family of solution 1. [x-y arctan(y/x)]dx + x arctan (y/x)dy = 0

A: Solution is given below:

Q: Q.1\Find (1) I=S tan³(5x) sec²(5x) dx. (2) =S dx x3+2x3+1 Q.2\ Find if y = lIn sin (x) cos(x*).V1+x)…

A: As per our guidelines I am solving only first question please resubmit other questions.