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Q: cosysin2xdx – (cos?y – cos?x)dy 0 when y(30°) = 30° %3D %3D -

A: Solution is given below:

Q: dx √ 1 + x² Using three point Gaussian quadrature formula, evaluate

A: Please find step by step answer below:

Q: F. Solve: y" – 6y' + 15y = 2 sin 3t, y(0) = –1, y'(0) %3D -

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Q: b) Z = Arctan ( x² /y³)

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Q: Find y': y = arctan(e2x) 2e2x y 1– e4x? 2e2x y = 1 – e4x %3D 2e2x y 1 + e4x %3D 2e2x y 1 + e4x2

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Q: Find dy/dx in terms of x and y if ax' – by = c°. Assume that a, b and c are constants.

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Q: If x1/3 + y1/3 = 4, find d2y/dx2 at the point (8, 8).

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Q: d) y" + y = sin 2t, y(0) = 2 and y'(0) = 1

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Q: If – 3x + xy – 4 = 0 then find dy da? at the point (-2, 1) in simplest form.

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Q: Se" cos 2t dt ,7L

A: integration.

Q: п sin ydx + cos²xdy = 0; y (÷) =| %3D 4

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Q: y" + 4y = cos(t−3)+4t, y(3)=0_y (3) = 7

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Q: dy If y = esr+11 then- dx 8e8x+11

A: If function is efx,  then its derivative is f'x efx

Q: 4x + Vx Y = (a) 7x2 – 3 et (b) y = 7x³ cos x 19

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Q: d²y dy and dx Find if x = sin 3z and y = tan23z dx2

A: It can be observed that both the variables x and y are the functions of  z, therefore to find the…

Q: 2e2x -1 Let y = %3D et dy Find dx

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Q: d²z et Ze2x Tan y Find- and dxdy d²z dydx

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Q: f(t) = e2t – 2t² cos 4t + 3t sin 6t – 2t + 5 %3D -

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Q: #5 ở V - (2xy sinz) - (3y~); + (5x> y? z?)k .* and vx ů. ealeulate

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Q: dy if y = Find dx et %3D 4x2-3x+2

A: Differential of function

Q: Q4: Find by using udv method cos bx dx ax

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Q: (b) Use the substitution u = x In y to solve the equation (ry + 2ry In² y + y In y)dx + (2x² In y +…

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Q: Given z = 11t - 48 and y = 121 sint dy da dy dx2

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Q: L sinh-t %3D .a 3s2-4 6. .b O 9s2 -4 .c O s2-4 3. .d O 2s2-4

A: We know that  L( sinh(a)t) = (a)/(s^2 - a^2)

Q: nd the tallawing differentu equation =d -1Sx +7 +eX cos(3x). the beral

A: The general solution of the given question has been solved below.

Q: Sfo sin (y²) dA, D= {(x,y) | 0<x<y, 0<y<26}

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Q: S. S. (x + 2y)dydx = 10, Jo a

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Q: Sove for dy 4 X3 hy= e*csch (2-y?)

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Q: Q NO3)IF y=Jsinx + Vsinx + Vsinx + . then show that(2y-1) = cosx .And Also Find dx (5vcosx) dx

A: Our objective is to find the derivative of above functions.

Q: Q4: Find by using udv method ax cos bx dx

A: Here I am attaching image so that you understand each and every step.

Q: (D5+3D + 4D³ + 32 cos (2a) + 3e 12D²) y = 16 sin (2x)

A: The given differential equation is…

Q: Calculate , ešlx²+9y dx dy, where Dis the interior of the ellipse () + (5)´ < 1. (Use symbolic…

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Q: Solve the egjuation ditferential (2x-3y+5)dx+(3x-2y+2)dy=0

A: Given the differential equation is                     (2x -3y +5)dx + (3x -2y +2)dy = 0

Q: a. y = (u /5) + 7 and u = 5x - 35 dy Find du

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Q: If y = cos24x, find dy/dx. a. 2cos4x     b. 2sin4x c. -4sin8x    d. -8sin4x

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Q: 9. (х +у) dx - (у -х) dy %3D0; у (1) %3D1

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Q: Y"-2y'+2y=e^2x(cosx-3sinx) by using  Variation of parameters

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Q: Find formulas for dy and Ay if y = 7x – 7. %3D - dy = Ay =

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Q: -dnd auf for the feaoy) =tan Cx+y). 3xし y

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Q: y = Ax tan(X), an dy 3T+3 %3D Find A. 6. 5 7 4.

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Q: Evaluate В: А: 3e-422 dz Jye-y dy 0, 0,

A: In the question it is asked to calculate the integral of two functions given below: ∫0∞ye-y3dy…

Q: z) tan(y2 + %3D

A: Given that, wx,y,z=tany2+4zx3x=r2t2y=r2tz=rt2 Then we get,…

Q: Solve osdinary DIPPedential Eguation + qy 6 Cos(3t) Y(0) = 0 %3D Y'(0) = 0

A: Consider y=emt be the solution of the homogeneous part. The auxiliary equation is m2+9=0. Solve the…

Q: Solve by substitution of u = Ax + By +C  dy/dx = (x + y +3)2

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Q: | 3yVT – 3y² dy

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Q: Q4 Find y'of y = In- %3D ? 1+e0

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Q: dy 2 ,? cosx +-y = -x²y dx %3D

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Q: π ,t<. 3 b) Let y(t)= 1? + sint , find L(y(t)) 3

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Q: by (3x? + y²) dx+ (2.xy) dy 7. C: 3D1 from (3,0) to (0,4) %3D - = 1 6.

A: We are given the following integral:∫C(3x2+y2) dx + (2xy) dy over the path C: x29+y216 = 1 from (3,…