pt of y=x3-4x2+x+6 В. -3,—2. and 1

Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. xydx - (x + 2)dy = 0

A: Given problem:- Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS.   xydx -…

Q: y= cosV1- x y' = V1-x² ² y' = 2v1- x² y' = 2va- x2 y' = Vx-x* 1 y' = 2Vx-x2

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Q: dz and dy dz 3. If x? – 3yz2 + xyz – 2 = 0, find -

A: In this question we have to find the dzdx and dzdy.

Q: dy りー! り(-)ニ。 x+3 2, xy' =1+X ら(4)=0

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Q: 4. f(x, y) = 10x²y* – 6xy2 + 10x2; fx(x, y), fy(x, y) %3D -

A: Consider the given function as fx,y=10x2y4-6xy2+10x2

Q: Use separation of variables to find an explicit solution. xyy' = 2xy² + y² %3D

A: Follow the steps below to solve a differential equation by the variable separation method. First,…

Q: 2 √2x-x² SJ J² J²^ √√√x² + y² + 2 00 y²)[2x − (x² + y²)]dydx -

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Q: Obtain the general solution using variation of parameters y''+y = (csc³x) (cotx)

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Q: 5-4y2 dy 3+2y

A: To evaluate ∫5-4y23+2ydy

Q: Find dy for given Values OF x and AX y= 4x315x X=-3 and AX = 0.3

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Q: 2) y' – (cotx)y = -(2cosx)y2 %3D

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Q: nclosed by x = y, x = 2 - y and the x-axis?

A: And: 5/6

Q: (ost) X= 3サ-3 DiD X-2-2y ¥ーにh で3,0) D3 Dy メーと2 サ=スメート X-4 <-リ-3 toノー4)

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Q: If f(x,y.z)= In(x2 +y³ +2z5), Find and dx² dz2

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Q: 2x X 5) i dydx y 1 x

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Q: find dy/dx

A: Known formula: ddx∫rxqxftdt=fqx q'x-frx r'x.

Q: 3. /4(1-)esc (1-y)dy

A: We have to solve the integral

Q: 4. y = vx +2 %3D x,for - 2 < x< 2 2, for x22 (x-1,for x< -2 5. y=

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Q: x = 2 + 3t, y = cosh 3t , 0 <y<1

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Q: max z = 2x + 8y %3D s.t 3x + 9y 12 х, у > 0

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Q: 2. T1: R2 - R2, T1(x, y) = (x – 2y, 5x + 2y) T2: R2 - R2, T2(x, y) = (0, x)

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Q: dy 15 +4y-042

A: ∫115+4y-4y2dy

Q: V2x-x2 SS2*-*" (x² + y²) dydx

A: Changing cartesian to polar coordinates: x2+y2=r2x=rcos θy= rsin θ x ranges from 0 to 2y ranges from…

Q: -x+y+2z = -3 3x- y+z = -2 2х- Зу- 42 %3D 1 X = y =

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Q: y = sec* ( Vsin(2t)) sec³ 3.

A: The objective is to find the derivative.

Q: 2. Differentiate the follow a) y = e 2x -ex %3D ex

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Q: xyz 9. f(x, y, z) = x² + y2 + z2

A: Givenf(x,y,z)=xyzx2+y2+z2To find Domain of above functions

Q: Obtain the particular solution. y' = x exp(y-x²) ; when x = 0 , y = 0.

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Q: 4. y=6-ax-x", y = x+l6, about the a %3D | yaxis

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Q: V1-x² 1-x²-y² e-3(x²+y²+z²)² dz dydx a) Evaluate

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Q: ed by F(x, y) = (-: %3D

A: The function given is , F→x,y=-x,y. Draw the table for the points plot on the graph for the vector…

Q: suonenba 5x mons: (1) +- = 3x + 3 (ii) x + 7x + 12 = 0 In (x +4)- In (x*) = 4 = 15 (iii) %3D (iv)…

A: Simplification

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Q: F(x,y) = -41² - 2xy-4y² +z+y.

A: Follow the procedure given below.

Q: y= x^4-3x^2+4x-3 find derivativr

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Q: Find y' for x°y* + 2x + 2y = 128 at the point (2, – 2). At (2, – 2), y' = Preview -

A: The given equation is: x3y4+2x+2y=128...(1) To find y' at the point (2,-2).

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find dy ().-0 (27). and X

A: Given 3x2-y2=t2 and y=tsinθ

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Q: 1. V2 3y 8-x2-y2 رار 0 0 x2+3y2 dzdxdy

A: We have to evaluate the integral.     According to our guidelines we can solve only one question so…

Q: 4. x = 9-y2 ,-2 <y S2 about y-axis vis

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Q: Find dy and simplify whenever possible. 1. y=(5-6x)¹2 4x-5 2. y=--- 2x + 1 3. y=(2x+5)(4x−1)

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Q: 31-x 2. Evaluate [(x+ y)dydx . 1 0

A: To solve this question first we integrate w.rt dy then put limits and after this integrate with dx…

Q: Evaluate S. (x – y)dx + xydx where C is the y = 2x2 – 1 from the point (-1,1) to the point (2,7).

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Q: Evaluate B: А: Vye-y° dy 3e-4z2 dz 0, 0,

A: There is a general integral that gets calculated with the help of β function. The integral is…