x - y -2x Prove by definition that for f(r, y) fy(x, y) = %3D x+ y' (x+ y)2

Q: (a) By using thẻ chain rülé and the dérivative (1, (1xl) = {"1, if x>0 if x<0' d %3D dx 1-1, find -…

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Q: (x – cos y)dx – sin ydy = 0 Of (x, y) = -xe-# +e-* cos y + k (y) ;f (r, y) = -e- sin y dy +k (y) Of…

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Q: Find dy and Ay for y = 3/x –1+ 2x at x = 2 with dr = Ar = 0.2.

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Q: Obtain the general solution of y√(1+x^2)dx+ x√(1+ y²)dy = 0 using variable separable method.

A: solution is given below..

Q: Reducible to Homogenous method dy X-y-3 x-y-1 dx

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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: 5х-1 dx that satisfies the condition F(1) =1. J 2(x-2) Find the Antiderivative F(x) = x²(x – 2)

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Q: If sin(x) f(x)= 68+t2 dt Jtan(x) and g(y)= f(x) dx , Then g) is equal to

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Q: 2) Obtain the DE with respect to x of (x - h)² = 4(y-k).

A: Sol

Q: Find the valve of k so that (2y sın x cos x -y + 2 y e** ) dx - (x - sın' x + kxye*) dy 0 becomes…

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Q: Q1-Use the chain rule to express dy / dx in terms of xand y: 1-1 a) y = аnd x = at 1= 2 1+1 b) y=1-…

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: Solve ODE for general solution: (2ysin(x)cos(x)-y+2y^(2)e^(xy^2))dx=(x-sin^2(x)-4xye^(xy^2)dy

A: Hence the given ode is exact. Obtain the general solution as follows,

Q: (b) Solve the integral [(3x – y)dx +(2x +3y)dy along the curve x = y' from (0,0) to (1, 1).

A: Solution of question as follows

Q: (b) Compute the partial derivative fy at the point (x, y) = (1, 1), or show that it does not exist.…

A: Let f:R2→R  be the function   F(x,y)=x-1.y-113(b) compute the partial derivative fy at the point…

Q: 2. Let f(x, y,2) = z-sin(xy), x = t, y = In t, z = e. Find derivative of f directly and by using…

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Q: 2, 0 1

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Q: Verify that [(y- 2x \dx +(2xy +x*dy = [S -川- dA where C is the bounda ôy R defined by y = 0, x = 1,…

A: See the details solution in below

Q: The integrating factor of the DE   y(2x - y + 1) dx + x(3x - 4y + 3) dy = 0 is

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Q: Integrate f(æ, y) = e2=² + 2y² over the domain {(x, y) | æ² + y? < 3}

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Q: Q4/ 2x 1- If z = f(x,y) and z = x²y³ + + 1. Determine the total differential. -"/2 2- Evaluate: 2 S*…

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Q: - Find dy at x = -1 if y=u³ +5u-4 and u = x² + x. dx

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Q: The order of the differential equat 2x2 - 3+y = 0 dy + y = 0 dx2 dx O not defined O 2

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Q: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

A: Please see the answer below.

Q: For f(x,y,z)=3xy+2y+8z - cos(x²+y²–z), the partial derivative fxy(1,2,5)=

A: Given function is fx,y,z=3xy+2y+8z−cosx2+y2−z. We have to find the partial derivative fxy1,2,5.…

Q: The integrating factor of the non-exact DE: ydx – (x + 6y²)dy = 0 is x-2 y-2

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Q: Reducible to Exact (y3+2exy)dx+(ex+3y2)dy=0

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Q: b) Obtain all the first and second order partial derivatives of f(x,y, z) = e* sin In yz + e sin In…

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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: The Integrating Fachor for the DE y dx- Ge-2x)Jdy -2y None of These

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Q: 4. Given xy+x*y=2 such that d/dt =2 in/sec. Find dy/dt for x= 1

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Q: An integrating factor of (x³y² + x)dy + (x²y³ – y)dx = 0 is (a)수 (b) (c) (d)을 2xy 2x

A: Given differential equation is x3y2+xdy+x2y3-ydx=0

Q: find the first partial derivatives of the function f(x, y) = integral from y to x of cos(t^2) dt

A: the given function is , f(x,y)= ∫xycos(t2)dt

Q: 2. Let L:= D2 - x-D+4x2. Verify that Ly 0 where y(x) = sin(x). %3D %3D %3D

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Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

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Q: (2) An integrating factor of (xy³ + y)dx + 2(x²y² + x +y*)dy = 0 is (a) y (b () (d) 2xy

A: We need to find an integrating factor of xy3+ydx+2x2y2+x+y4dy=0 Now, a differential equation of the…

Q: 25. (y cos x + (2y sen x – xr + In y) dy = 0, y(0) = e 3xy – 2x) dx –

A: The given differential equation is: y2 cos x - 3x2y - 2xdx+2y sen x - x3 + ln ydy=0  ;…

Q: ution of yl = x+xy2 W

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Q: 1 The partial derivative of f(x, y, z) = Arctan with respect to z is xy? z³

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Q: The integrating factor of the DE (x^2 + y^2 + 1) dx + x(x - 2y) dy = 0 is

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Q: approximation of I = [" f(x)dx using composite Simpson's rule with n=4 is:

A: In this question, we evaluate the definite integral by using the composite Simpson's rule for n=4.

Q: Find the differential of the function y = In(S - 2x) 2dx dy = (5-2x) dy = (5 – 2x )dx -2 (5-2x)dx…

A: Given : The function y = ln(s - 2x).   To find the differential of the function y = ln(s - 2x).

Q: an f (b) For a positive integer n, find the n-th partial " azn derivative off with respect to z, for…

A: Solved below.

Q: Find the differential dy. x + 2 y = 9x - 1 dy =

A: In this question we have to find we have differentiation of y.

Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

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Q: 1. if z = a² sin[e!n 2y] + 3xy cos[e!n2x] – 4a?y², find the partial derivative of z with respect to…

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Q: a) Find the differential dy of y=x2+2x+5. (b) Evaluate dy for x=3, dx=1/2. (a) dy=????????? dx (b)…

A: GIVEN THAT y=x2+2x+5

Q: 2- y(x + y +1 ) dx – x(x + 3y + 2)dy = 0 Reducible to Exact Method

A: We have to find general solution of given differential equation which we reducible to exact method :…

Q: Find the differential dy. y =  x + 8 7x − 1

A: Assuming that y is given as:

Q: (b) Solve the integral (3x– y)dx+(2x+3y)dy along the curve x = y' from (0,0) to (1, 1).

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