(cos x cos y + 2x)dx – (sin x sin y+ is Exact equation صواب ihi

Q: Evaluate the integral given below

A: To evaluate the integral given below, ∫∫Rcosxsin2ydA, R=0,π2×0,π2

Q: How to compute Cp using below equation, OP, sin 0; Cp, = 2 sin? 0; +2 cos 0 dy dy Where y = 0.5x…

A: To simplify: CPi=2sin2θi+2dθdyisinθi∫0yicosθdy

Q: 2. Find y': sin(x+y)% y2 cos x.

A: As per our guidelines we are supposed to solve only one question i.e. the question number 2 . Which…

Q: 1 + cos x – 2xy): fip y(y + sin x), y(0) = 1. COS I 1+ y? dx

A: To solve the given exact differential equation.

Q: x = cos(30), y = 2 sin(0).

A: The parametric equations are given as, The the corresponding derivatives are calculated as,

Q: Evaluate the integrals.

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Q: cos 2x he ƒ -dx is 4+sin 2x {A} In|4 + sin 2x| + C {B} In|4 + sin 2x| + C {C}(4+sin 2x)² + C {D} -(4…

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Q: " + y = 12 cos 2x - sin x. A. " + y = sin 3x +4 cos x. A

A: Given: y''+y=12cos2x-sinx

Q: 2 cos x dx, 1+ sin x (c) t = sin r. 0.

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Q: Differentiate.

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Q: fe²x+Inx² sin x² dx = - +1/√√e²x cos x² dx

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Q: y'of y = e-2*sin 3x

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Q: 3. y" y'-y = cos(5t) - sin(5t); y(0) = 2 and y'=5

A: First find the commentary function then particular integral and then use the initial conditions as…

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

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Q: (1+sinx)9 cos x dx , u=1+sinx is The values of a. (1+sinx) 10 + C 10 b. (1+sinx)10+ c 1 (sinx)10+c…

A: Solution: The objective is to find the value of the given integral

Q: i) f si sin 3x cos 3x dx ii) [ cos³x dx

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Q: 19. y = -3 cos 2x 20. y = 5 sin 2 AAMA A

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: (f) ) (3x − 1)√√x² + 2xdx - (8) / sin". (h) [ sinh r cos adr sin x -dx √cos5 x

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Q: y cos x- sint x %3D

A: Given: Y = cos4x -sin4x

Q: sin' y 3 Find the particular solution of xsin?y cos y y' +: 1+In x = 4 :y(e) =

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Q: 5. (sin 0 – 2r cos² 0) dr + r cos 0 (2r sin 0 + 1) d0 = 0

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Q: cOS X sec x = 2 sin x if 0 Sx< 2m А. п/4, Зл/4 В. π/ 3, 5π/3 С. T/6, 5n/6

A: Given: cosxsecx=2sinx

Q: sinh(Inx)dx 1) 2) fe* sinade e*.sinxdx 3) sin? (2x).cos(3x) G

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Q: iii- y +y tan .* sin 2x, y(0) = 1. (Bernoulli Equation) %3D

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Q: (r + sin 0 – cos 0) dr + r(sin 0 + cos 0) d0 = 0 **

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Q: 5. x = cos 2t, y = sin 2t, 0 <t< T

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Q: [(cos 2y) – 3x?y²] dx + [(cos 2y) – 2x(sin 2y) – 2x³y] dy = 0 %3D

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Q: sin x = x (1 + tan y). Find and provide solution for dx/dy

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Q: I) sin X dy dx Sin 2X - y Cos X

A: Explanation of the answer is as follows

Q: 5. (4xy-y²+10x²+sin x)dx+(2x²-2xy+ cos y )dy=0

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Q: a) [ sin³(2x) cos(2x)dx (a) [ Sin(+) dx (b) [ Sin(F) dx dx (2 + e*)? dx |2+e*

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Q: 1. S x4+a4 dx x3 2. Jydy √a2-y2 3. I cos2tdt (1+sin2t)4 4. I tanßsec2ßdß 5. [(tan) – 1)2d0

A: We have to find  the value of given intregation.

Q: æ' = y – 5 sin (3t); y/ = -4x + 17 cos (3t) , ift = n, x = 7; y = -4

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Q: * sin x 2. SS y dydx ans: 4

A: Using Double Integration

Q: Find y' and y". y = cos(x?) y' - -sin (x²) ( 2x) y" =

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Q: 2) x³y? = 2x + 2y3 3) y = sin?(x) – cos³(2x) + 2 www. .

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Q: sin(x) d Find (S sin (4 t) dt). cos(2)

A: Use the concept of derivative of an Antiderivative.

Q: B sin 5x+ sin 3x 1 sin 5x+-sin 3x+c 6 I 10 fcos 4x cos.x dx = ?

A: Given :∫cosxcos4xdx

Q: (r+sin 0- cos 0) dr + r (sin 0 + cos 0) d0 = 0

A: (r+sinθ-cosθ)dr+r(sinθ+cosθ)dθ=0 lets rearrange and then integrate

Q: Exact Equation (cos x sin x – xy²)dx + y(1 – x²)dy = 0

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Q: cos(2y) – 3x?y²]dx + [cos(2y) – 2x sin(2y) – 2x³y]dy = 0 when x = 0; y = 0 %3D

A: Let's find.

Q: [2xy cos(x²) – 2xy + 1]dx + [sin(x²) – x²]dy = 0

A: The solution attached :

Q: e of y = -3 sin x + 5? (I Vミー

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Q: I sin(z) cos I) COS(2C (x) dx %3D

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Q: Find a general solution. Show the details of your work [3] yi = y1 + Y2 + 10 cos t y2 = 3y1 – y2 –…

A: See the attachment

Q: dy - x = x2 siny dx 3 -2 (-siny + cosy + Ce-y/2)* ANSWER: x = -

A: Note: Here, we shall solve Bernoulli's differential equation  dxdy-x=x32sin y instead of…

Q: y" – 2y' + y = [-6x – 8] cos(2.x) + [8x – 11]sin(() 2x) %3D

A: We have to solve the differential equation y''-2y'+y=[-6x-8]cos2x+[8x-11]sin2x.

Q: 1. Solve: sin z cos² y dr + cos? r dy = 0, y(0) : (separation of variables)

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Q: y = tan x sin (2x)+cos (2x) 2 y' = A sin (Bx) + Ccos(3x) 3. A = B = C =

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…