Euler's difFQ 3. (y()) =VZ Eq cal g'ral-2y cx ) =x (y (x )

Q: 4. (y? cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e %3D 5. (x2 - 1) dy =…

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Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

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Q: Find the differential dy of the given function.

A: Given :              The given function is :                   y = 9 - x2 To find :            The…

Q: Separable DE) y'ln² y + y√√x=0 y(0) = e

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Q: Let y = 4x2 + 4x + 3. Find the differential dy when x = 1 and dx 0.4 %3D Find the differential dy…

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Q: Use the Chain Rule to solve the indicated partial derivatives. Simplify your answers whenever…

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Q: 4. (ye"-2y)dx + (xe-6 xy- 2y)dy = 0; x = 0 when y = 2. 5. (x+3) cos y dx - (sin y In(5x + 15)-y} dy…

A: The exact differential equation for the equation, F(x,y)=C, is written as Fxdx+Fydy=0, where, Fx ,…

Q: Find the first partial derivatives of the function z = x sin (x y^2).

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Q: 3 - y cos xy - 4x ) dx + (- 2x+3y x cos xy + 2y) dy = 0 - | 2x+3y 2.

A: Compare the given equation with Mdx+Ndy=0 to obtain M and N. Calculate the partial derivatives of M…

Q: dy/dx=3x^2+1 with y(1)=2. Estimate y(2) by Euler's method

A: given differential equation dydx=3x2+1 with initial condition y1=2 claim- estimate y2 by euler's…

Q: Let y=5x2y=5x2.Find the change in y, Δy when x=3 and Δx=0.2   Find the differential dy when x=3 and…

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Q: Find the differential dy of the given function. y = 3x2 − 4

A: Given function is Differentiating with respect to x, we get Therefore , differential dy is

Q: 2. (2.xy – sin x}dx+ (x² - cos y ldy =

A: We will solve the given differential Equation.Below find the solution in the image.

Q: Find the differential dy of the given function. y = InV9 - x2 dy =

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Q: Q /Find the solution for the partial differential equation using Lagrange method az az + - ax = 2y…

A: We have the partial differential equation 2∂z∂x+∂z∂y=2y , where zx,0=cos3x If we have a partial…

Q: 2.Find the particular solution of y (9x-2y) dx -x (6x-y) dy=0., when x=1, y=1. Let x=vy

A: Find out the particular solution.

Q: Q6. Using Rule l-IV to find an integrating factors. (x² + y² + x)dx + xydy = 0.

A: Given- x2+y2+xdx+xydy=0 To Find- The integrating factor of the above differential equation.

Q: Find the first partial derivatives of f(x, y) = 4x cos(x2 + y?). %3D

A: Given fx,y=4xcosx2+y2

Q: 4. (y² cos x - 3x²y – 2x) dx + (2y sin x – x³ + Iny) dy when x = 0, y = e %3D 5. (x² – 1) dy = ((1 +…

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Q: 3. z = x+y x-y

A: Given:        z=x+yx-y Partial derivative with respect to x:      ∂z∂x=∂∂xx+yx-y      Treat y as…

Q: (y² cos x – 3.x²y – 2x)dx + (2y sen x – x° + ln y)dy = 0, y(0) = e

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Q: Find both first partial derivatives. g(x, y) = ln√x2 + y2

A: Given function is gx,y=lnx2+y2 Partial derivative of function is derivative of function with one…

Q: 3. Find dy/dx of: x'(x-y)-x-y evaluated at x = 0.001 and y = 0.002

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Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

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Q: 4. (y² cos x - 3x²y - 2x) dx + (2y sin x – x³ + Iny) dy = 0, when x = 0, y = e %3D

A: Note: According to our expert guidelines only one individual question is to be answered, kindly…

Q: Show that the function y =  A e-x    + B x e-x satisfies the differentialequation y"   +2y' + y  =0

A: The given differential equation is y''+2y'+y=0. Let y=Ae-x+Bxe-x. This implies that,…

Q: y (y^3-x) dx + x(y^3+x) dy=0_At· muon

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Q: -2x + 3x -x) dr- (sin y + y e (y e + +3y e) dy 0. x(0) 1 D 2r-- O 2y - y+ xr e O x+ 2x-y e-3y e+3e–…

A: The given differential equation is,(y2e-2x+3x2-x)dx-(siny+ye-2x+3yey)dy=0, x(0)=1

Q: Find the differential dy of the given function. y = √√√√9-x²

A: Given y=9-x2 we need to find dy

Q: dz Find dz -3 and of z = x³ In(1 + xy). dy

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Q: Solve the general Solution of:  (xsiny/x- ycosy/xdx)dx + xcosy/x dy=0

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Q: y' + 4y = e^(4t) %3D

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Q: -y cos xy - 4x) dx + (- x cos xy + 2y) dy o 1. = 0 2x+3y Zar+3y 2.

A: Proceed as shown below...

Q: a) dx dt dy dt =x+√3y+et √3x-y+e³t = ||

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Q: Q2. Solve y [xcos (e)- + ysin (:)] dx – x [ysin 2) – xcos (2)] dy =

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Q: Let y = 3x² + 8x + 3. Find the differential dy when x = Find the differential dy when x = 2 and da 2…

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Q: If f(x, y) = y² cos(x) – x³ In(y), find the second partial derivative ду дх

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Q: 5/(A)Evalute ex² dxdy. (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

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Q: dy = (x – 2)e-2y dx einitial condition y(2) = In(2).

A: Explanation and solution is given below.....

Q: 8. When reduced to a linear DE of order one in z, bernoulli' equation dy/dx +y (1/x) =3x2y2

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Q: y² cos x - 3x3y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e x² - 1) dy = ((1 + x)2 -…

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Q: Consider the nonhomogeneous differential equa 1 "(x) + y(x) = e '+ sin a

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Q: y = 3 Arccos ( 1 -)+ v6x – x² y= In (*+1), (x+2)3 x²(x+1), e2x-e-2x y = e2x+e-2x

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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: Find the differential dy of the given function. Xx + 5 y = 2х — 9

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Q: 3. Find dy/dx of: x'(x-y) -x-y evaluated at x = 0.001 and y = 0.002

A: The given equation is x2x-y2=x-y2 at x=0.001 and y=0.002.

Q: Find the differential dy of the given function.    y = x√(1 − x2)

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

A: Assuming that y is given as:

Q: ne differential ay of 'uonpuni y = V 5 - x2

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