Compute on your paper, showing all work: dy dx (i) = x + y (ii) y = xy + 2x² at the point (-1, 1) (ii) x³ – y = 4 (iv) tan(x + y) = xy at the point (0, 27)

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

A: Solving integral

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: t + 2y = t² – t + 1, y(1) - dx 2 dy 2 dx - y = 4 sin 3t, y(0) = 1 ||

A:

Q: Use Fubini's Theorem to evaluate .2 -dx dy. I + xy

A: Given :            ∫02∫01 x1+xy dxdy By Fubini's theorem, the above integral can be rewritten as ∫01…

Q: Find partial derivative of dx for the function f(x,y) given below exp 2x. siny .(at the point (In2,…

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Q: Find dy/dx for (x+y)3=x3+y3,at the point  (-1,1)

A:

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: dx =- 1. dt dy at x = 2 if y = 4x° – 2 and dt %3D Find - dy dt

A: Given: y=4x2-2 and dxdt=-1 To find: dydt, when x=2.

Q: 2(y+1) dy t 2) 2(у + 1)4 dx x+1

A:

Q: Find dy/dx for x*+siny = x'y

A:

Q: 7 Find dy (b) x siny-ycosx-y = 1. dx

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Q: Compute the differential dy for y = (2x + sin x)². dy =

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Q: dy Find for three only: dx 1) y = In(cos x . Inx²)

A:

Q: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

Q: Find a result by using exact for (sinxcosy)dx = -(cosxsiny)dy = 0 b. (x-6xy + y² + 10)dy = -(x² -…

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

Q: Obtain the general solution using separation of variables x cos² y dx + tan y dy= 0

A: Given differential equation is: x cos2y dx+tany dy=0 Apply variable separable: tanycos2ydy=-xdx…

Q: Find dy dx2 by implicit differentiation. x y + eY d2y %3D dx2

A: Note: As per company's guidelines, we should solve only one question. So, kindly post the next…

Q: solve the IVP x(1-siny)dy=(cosx-cosy-y)dx y(π/2) =0

A:

Q: Let y = tan(4x + 6). %3D Find the differential dy when x = 5 and dx: 0.4 %3D Find the differential…

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Q: Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dy dx…

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Q: Solve the DE sinx siny dx + cosx cosy dy - O by separation of variables. A sinx cosy - C sin y B cos…

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Q: d²y 1.) of y = sinInß and x = In(Inß) dx2

A: Topic = Derivative As per guidelines , At a time only one question can be answered out of different…

Q: Let y = tan(5x + 2). Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

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Q: Find dy/dx of y=sin-!x+cos -!x dy/dx is Blank 1.

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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: Explain why the linear approximation to ƒ(x) = cos x at x = 0 is L(x) = 1.

A: The linear approximation, or tangent line approximation, of f at x=a is defined as Lx=fa+f'ax-a This…

Q: Find dy/dx by implicit differentiation. x3 + y3 + 5y - 6 = 0 %3D dy/dx = %3D

A: given equation is -  x3+y3+5y-6=0

Q: (cos y- zsee'y) de – sin y dy = 0

A:

Q: Q) - Find of y = sin de dy ! -11

A: Siny = 1/x.

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: dy Find at x = dt dx - 1 if y = 2x? – 3 and dt - 2. dy dt ||

A: y = 2x2 - 3dxdt = -2dydt = ?   at x=-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: cos(2y - x) = 3ysin x

A:

Q: Let y = tan(2x +5). Find the differential dy when x 3 and dr = 0.1 Find the differential dy when z =…

A: Given that y=tan(2x+5) find the differential dy when x=3 and dx=0.1 find the differential dy when…

Q: Let y = tan(4x + 4). Find the differential dy when x = 5 and dx 0.4 %3D Find the differential dy…

A: Given : The function y = tan(4x + 4)   To find : Differential dy when, 1. x = 5, dx = 0.4 2. x =…

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (8, -3)

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Q: dy Differentiate parametrically to find dx in terms of t: 1 y = 2t2 + 4 X = |

A: x = 1/(t-1) y = 2t2 + 4 We have to find dy/dx

Q: - sin y, dz = cos x dx – cos y dy

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

Q: S. use "Exact Equation" method (cosxcosy + 2x)dx-(sinxsiny + 2y)dy = 0

A:

Q: Find the differential dy of the given function Y=arctan(x-5) Dy=?

A: Use the standard derivative of inverse trigonometric function and chain rule.

Q: Let y=3sqrt(x) Find the change in y, Δy when x=2 and Δx=0.3 Find the differential dy when x=2 and…

A: We are going to solve

Q: Find the differential dy of the given function. sec² x y x² + 2 sec 2x (2x²tan x + 4 tan x-2x)…

A: This question is based on quotient rule

Q: dy ху* - сosx sin x . У (0) -2 y(1–x²) dx

A:

Q: V4-z2 z siny dx dz dy 16 3. 16 5 0 16 0 66 0 66

A: The objective is to solve the integral ∫0π∫02∫04-z2z siny dx dz dy

Q: dy Find dx by implicit differentiation. 3 +y = 25 -1 dy 9x а. dx 4y dy b. dx 4x Зу -1 dy 4х с. dx 1…

A: We need to find dydx of x23+y32=25. So,                 x23+y32=25Differentiating both sides wrt…

Q: What is the I.F of (x^2y^3+2y)dx+(2x-2x^3y^2)dy=0?

A: Find the integrating factor

Q: Can you help me step by step?

A: Given information:

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

A:

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (4, -3)

A: To solve the given line integral.

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.