Evalute I = - | x cos(2²) +x sin(r²) dr

Q: Integrate -- | cos 5xcos x a) 0.5 b) c) d) 2

A: We can use the trigonometric identity, cos A cos B=12cosA+B+cosA-B . Use the integration formulas,…

Q: Solve for the general solution of (cos x cos y – cot x)dx – (sin x sin y)dy = 0.

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Q: (b) (cos(x) (2x + 3))'

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Q: 1. sin'y (2-3 cos y )dy

A: Given: ∫sin3y(2-3cosy)2dy

Q: Solve: Tanxdy+ y°Sin²xdx=0, y(0)=1 а. у"(3-Сos2x)-2 b. у(-2х + Сos2х) -1 d. y(-1+ Cos2x) — х с. у?…

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

Q: -3x cos 2x da A) - cos 2x - 3x sin 2x + C B) - 2x- sin 2x +C s 2x - sin 3x + C D) - cos 2x - sin 2x…

A: Since you have posted multiple questions . As per the guidelines we will solve the first question…

Q: SOLVE THE EQUATIONS

A: Given:

Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: Solve the initial value problem : f'(x) = cosx + sec²x, f (÷) = 2 +÷. %3D

A: Solve the differential equation by separation of variable and use given initial value to eliminate…

Q: nx and y=cosx from x=- to x=- 4 4

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Q: Solve for the first-order DE: y’+y-y^2(cos2x-sin2x)=0

A: Solution: A first-order Bernoulli ODE has the form of y' + p(x)y =q(x)yn Rewrite the form of…

Q: y f(x)sin2x + g(x)cos %3D x) =tan3x x)% sin3x %3D - r) =cos3r

A: Differential equation: y''+9y=tan (3x)The auxiliary equation is,m2+9=0m=±3iComplementary function…

Q: y = (sin x +cos x) sec x = sec² x

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Q: fo (9 cos(x) – 2 sec²(x)) dx

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Q: ¥2/3 6. cos'x sin x dx 5.

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

A: Solution is given below:

Q: cos2x a) -.dx,b) xe*. dy Į sin2x. [In(sin2x)]² + sin2x 0.

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Q: (i) y = x® +- vx ++ 2 4 -Vx + + 10 | (ii) y = sin (cos(x2 + x)) %3D

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Q: y = Ceax cos(bx) + C2eax sin(bx); a and b are parameters y = Ce2x cos(3x) + Cze2* sin(3x)

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Q: (a) / sin sin(8x) + cos(7.x) dx (b) / (3x – 5 sin dx 2 (c) / cos(3t) + sin(5t) dt

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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: 3. = Cos xsin +xax+a 5/2 3/2 1. Ans: Y= 4sin'x* sinx+ To CAx+4)^- Cax+a) 3.

A: To solve: dydx=cos3x sin2x+x2x+1 Solution Given differential equation can be written as: dy=cos3x…

Q: find δƒ/δx and δƒ/δy. ƒ(x, y) = cos2 (3x - y2)

A: Consider the provided provided function, fx,y=cos23x-y2 Find the partial derivatives of the function…

Q: I. Eliminate the arbitrary constants -3x y= C, e sin2x + - 3x Cze cos 2x

A:

Q: The minimum value of cos x +3 sinx+ 5 is: - V10 А в 5 - 10 5+ V10 D 5 E -5 - v10

A: let fx=cosx+3sinx+5if we have to find minimum value of function then first derivative equal to zero…

Q: 2 cos(플x-지) =D v2 TO

A: Given trigonometric equation is:  2 cosπ2x-π=2 We have to solve for x.

Q: i. Jsin xcos 2x - sin 2x cos xdx

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Q: 3x 2. y = Ae³x cos x+Be³x sinx

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Q: x - ; )* ( sin 2t X' |X + 4 2 \2 cos 2t)

A: We have to solve the system of equations.

Q: .2. COS X sın.x.ços.Xdx

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Q: 2. y = ₁³x cos x + c₂e³ 3x Ge 3x sinx

A: Find out the differential equation by elimination of arbitrary constants.

Q: 2y 1 + cos 3x - 4.x + 3y sin 3.r = 0 %3D dr

A: 2y-1x+cos3xdydx+yx2-4x3+3ysin3x=0 Rewrite the above ODE in the form of Mdx+Ndy=0.…

Q: x cos x² 2. X C0 dx -siny

A:

Q: Solve the initial value problem : f'(x) = cosx + sec2x, f(÷) = 2+. %3D

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: y = cos x, y= sin 2x, x = 0 and x = 2

A: Solution

Q: QIN Evaulate : f v2 + cos4t sin4t dt

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Q: (xSin 受)x x cas dy -y Cos X Cos

A: Thr solution is given in the next step.

Q: 2 cos Vx = cos (2x-1) 0<xs1

A:

Q: 2ク • *ý-4xý +6y =-X sinx 3 2. Ans y= C,X +C2 X+X Ssinx

A: We have to find the solution of the give second order differential equation

Q: solve the nonhomogenous equation y''' - 6y' = -cos(x)

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Q: Differentiate y= e*cos (x2): y' = A -e*sin(x²) e(cos(x²) – 2 xsin(x²)) e*cos(x?) – 2 xsin(x²) D -2…

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Q: y = cos 3x a. 3 sin 3x b. - sin 3x c. sin 3x d. -3 sin 3x с.

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Q: b- y" -y+2y+ cos x, 05x y(0) -0.3, y()--0.1

A: To show the boundary value problem has unique solution we solve the given ode by method 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: e-3t sin (4t) y (0) ==

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Q: e3x [7 sin 7x + 3 cos 7x] +C 58

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

Q: Determine the general solution of (cos(x)cos(y)-cot(x))dx=(sin(x)sin(y))dy

A: Given: cos(x)cos(y)-cot(x)dx=sin(x)sin(y)dy

Q: n3xcsC3X)ax 3. S sin2xcsc3x+cos²xcsc3x

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…