cos(x + y)dx + (3y ^ 2 + 2y + cos(x + y))dy = 0, with the boundary condition of y(1) = -2.

Q: find the integrating factor of cos(x)y'+sin (x)y=2cos^3(x)sin(x)-1

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 9xyz + 10yz²…

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Q: If f(x, y) = y° cos(x) – x³ In(y), find the second partial derivative ду дх .A ² f ду дх 3x2 -2y…

A: Calculate partial derivatives

Q: Find the differential dy of y=√x. Show complete solution

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Q: (1) Find the general solution for -) dx - -) dy = %3D

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Q: Find a function w = ƒ(x, y) whose first partial derivatives are ∂w/∂x = 1 + ex cos y and ∂w/∂y = 2y…

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Q: Find the general solution Using Integrating Factors Found by Inspection. Show complete solution.…

A: Find the general solution Using Integrating Factors Found by Inspection. Show complete solution.…

Q: 6. sin'x dx 7. cos*x dx 4x+ 2 dx x +x + 5 8. .2 (1+x*)dx 2x-1 dx 2-8x + 15 10. 2x+x +1 1. dx (x-1)…

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

Q: 3. (16x + 5y)dx + (3x + y)dy = 0 1 (Cos 2y - 3x²y²)dx + (cos 2y - 2x sin 2y - 2x'y)dy 0 the

A: In the given question we have to find the solution of the differential equation 1.…

Q: 2 xy dy – (r' + 2y³) dx = 0 xsin 2 dy y sin- -x | dx

A: Homogenous differential equation: Let us consider differential equation of the form…

Q: From the partial differential equation by eliminating the arbitrary functi on s f and g from = z =f…

A: Given: z=fx+ct+gx-ct

Q: 3y dx 2 (2y In +3 sin y]dy =- + 3 Sin Y X+ 3

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Q: For the function f(x, y) = Vx³ + y³ find both partial derivatives at the point (0,0) (separate by…

A: Given function, f(x,y)=x3+y33

Q: 2. [2x*tan y – ysin (2) – 1] dx + [xsin (2) + x*sec*y] dy =

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Q: dy/dx of y = (x^2)cos^4(x)

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Q: (cos 2y-3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0

A: Given : Differential equation cos 2y - 3x2y2dx + cos 2y - 2x sin 2y - 2x3ydy = 0   To find :…

Q: What is an integrating factor of the nonexact DE  (2y^2 + 3x) dx + xydy = 0 ?

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Q: 4- Find dy/dx for: d- y = /1+ sin³ (x5) e- y = 2(Va – 1)( f- y = cos³{sin(2x*)} x-2 x²+3x' %3D

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Q: What is the integrating factor of (y – cos² x) dx + cos xdy = 0?

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Q: 2. Cosh X y sinh x 2 cosh x sin dx dy dxxy = 1 5. (1-x)

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Q: If f(x, y) = y cos(x) – a° In(y), find the second partial derivative ду дх .A 3x2 = -2y sin(x) ду дх…

A: Option (a) is correct.

Q: Find the indicated partial derivatives. y+ Sz az dy ex

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Q: (2(1-2) (1--) dy dx dz 1-z) Evaluate S, a-2 (1-

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Q: Find the first partial derivatives of f(x,y) = 2 ex"y of II

A: Consider the given function. fx,y=2ex10y The objective of the problem is to find the first partial…

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: f(x, y) = ex + tan(x + y2).

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Q: Find the particular solution of the differential solution dy/dx=x^2(y+2) given that the point (0,5)…

A: Given,  The differential equation  dydx=x2y+2   Point 0, 5 lies on the graph of the solution  We…

Q: A/ Integrate TWO only 2x dx 1) S- 2) S 4e cos4x dx 3) x In(x + x)dx x +x+1 B/ Ali is filling a cone…

A: As per the guidelines we can solve 2 problems

Q: From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)

A:

Q: The integrating factor of Linear differential dy equations + y × 4 tan x = sec²x is dx . O tan 4x O…

A: To find the integrating factor for the below linear differential equation. dydx+y×4tanx=sec2x

Q: 6. Use separation of variables to find product solution of u(x, y) for the partial differential…

A: Given,            ∂2u∂y2=∂u∂x+xu                        (1)

Q: Find both first partial derivatives. z = In əz əx az ? ду II

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Q: dy 1- cosh x dx + (sinh x)y = e-x - 2 dy 2- - y = e*/2y3 dx

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Q: Find both first partial derivative h(x, y) = e-(xª + y^) hx(x, y) = hy(x, y)

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Q: Integral of | 4sinxcos cos |dx 1. J sin 9x cos4x dx J cos 2x cos (-x)dx 2. 3.

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Q: (y2 cos cos x – sin x)dx + (2y sin x + 2)dy = 0 -

A: The given differential equation is first-order non-linear ordinary differential equation:   First we…

Q: Find all first partial derivatives. z = ln(x2 + y2 + 1)

A: Given The equation is  z = ln(x2 + y2 + 1) .

Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

Q: Find the value of dx at the point (1,1,1) if the equation 6xy + z"x-2yz = 5 defines z as a function…

A: Given: (x,y,z)=(1,1,1) and z=6xy+z4x-2yz-5=0

Q: Find all the second partial derivative T = e-4r cos(0) -4r, Trr 16e 'cos (0) %3D Tre = 4e -4r,…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: v = exy In(x +y)

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Q: (siny - ysinx) dx +(cosx +xcosy) dy =0

A: We will use the method of exact differential equations.

Q: Use separation of variables to find solution for the given partial d²u differential equation 4- -…

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Q: Find the mixed partial derivative at the point (2, 3) for h(x.y) = x sin(y) + y sin(x) + xy

A: The given function is, Differentiate the above expression with respect x partially.

Q: Determine a region of the xy-plane for which the differential equation = y – x² would h dx unique…

A: Given, the differential equation                               dydx=y-x2

Q: 1. (sin y — y sin x)dx + (сos x + х сos y — у)dy 3 0 %3D 2. (1— 2x2 — 2х) у' %3 4x3 + 4ху 3. (Зx cos…

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Q: {dy}/{dx} for y=4sin^{-1}(x^2)

A: The explanation of answer as follows

Q: (b) Find the partial derivative, g where g(x,y)=sin' (2x+y). (c) Given z= In(2x+3y) with x 2s' (t-s)…

A: