If (4x + xy):(5xy - y*) = 12:5, find x: y

Q: 2. If F = (3x² - 3yz)i + (3y²-3xz)-(32²-3xy find div curl

A: Given problem:-

Q: from y = ae + be %3D 2.

A: y=ae4x+be-4x ....(1) Differentiate both side w.r.t x dydx=4ae4x-be-4x        ....(2) From (1) and…

Q: compute ∫_D 2ydx+3xdy, where D is described by 0≤x≤1, 0≤y≤1

A: Green's Theorem: Let C be a positive oriented, smooth, simple closed curve. Let D be the region…

Q: 7) Suppose y varies directly with x. If y=2 when x = – - what is y when 2 X--0.3?

A: Given the data :

Q: Solve Ytt = = 4yxx 0 0 Yx(0, t) = 0, Yx(1, t) = 0, Y (x, 0) = 0, y(x, 0) = 3cos(2nx)

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Q: 31. If 9x² = y(y – 3)², show that (y + 1)² ds - dy². 4y

A: We know that Given Firstly, we find dx in terms of dy

Q: Integrate (1/ (3x + 4)) with respect to x and evaluate the result from x = 0 and x = 2.

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Q: (5+2y)* dy

A: (6) Given- ∫-2-35+2y4dy To find- The value of the above integral. Identity Used- Using the power…

Q: [d] If xz = yz and z - 0 then x = y

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Q: I have equation 3x(y-x)=0. Is it true that x here is equal to 0 and y is equal to x? How can I show…

A: To check:  Whether x here is equal to 0 and y is equal to x. Given information: The equation is…

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+C₁e-ax using 2…

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

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Q: Find ƒyxyz if ƒ(x, y, z) = 1 - 2xy2z + x2y.

A: Given that, fx, y, z=1-2xy2z+x2y           ...(1)

Q: f(x, y) = In(4x + 3y) Calcule

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Q: f(x, y) = In(4x² - y) %3D

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Q: Find dy. y=5th root of x^2(8-2x)

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Q: If x < 0 and y > 0, determine the sign of the realnumber. xy2

A: Given that, x < 0 that is x is negative. y > 0 that is y is positive.

Q: 7. dz | zV 36z2 - 25

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Q: 8. = In(3x² – 2y + 4z³); x = 1/2, y = t²/3, z = 1=2 w

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Q: Xxy-Z = Gauss eleminatin %3D 2X -y42=5 -x +2y+23 or

A: We have to solve given problem:

Q: (2-x²) y" + 2xy' - 2y = 0 olution to

A: Given differential equation is 2−x2y''+2xy'−2y=0.....1. a We have to verify that y=x is a solution…

Q: 4y² – 25 -dy

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Q: Show that Inx dx = -/Zn². x3/4(1+ x)

A: The given integral is: ∫0∞lnxx341+xdx

Q: Evaluate: ₁²-du So -3 (x² y²)²7 x+y du dt

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Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using 2…

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Q: x^2=Axy+By

A: Simple value put

Q: 9. If x2-xy + y2 = 3, find y' and y", %3D

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Q: b) y = In(xeVx + 2)

A: The solution are next step..

Q: 2こx+iy 2 Recz) =l 3-i1 if 121 =2, then

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Q: 7 dy if Xy+2x +3y =1

A: We use implicit differentiate method to find dy/dx.

Q: y" – 1/x = 0; y = x In x – 5x + 7 -

A: This question can be solved using the concept of first and second order derivatives.

Q: ind y1

A: Given, y=7-x23

Q: 3 If y=/xL5x²_36 x²_3x²+Yx-12 (3 14 shuw that dy 24 dx4

A: firstly simplifying these expressions then , use the concept of differentiation

Q: 2₁ "+21y+8x=y" + 5y' + ex

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Q: Compute ƒxxx and ƒxxy for ƒ(x, y) = x3y.

A: Given function - f(x, y) = x3yConcept - While partially differentiating with respect to x, other…

Q: O y'+ (oy -asin 8t y W): -1 2

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Q: 3)으 rcose de Jsine 1-x2 d ¿= xp 2

A: LEIBNIZ RULE

Q: af(x,yz) -

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Q: Find of z = 2x° 5xy" + x¯ y dy2 -10ху + 3x? у? = -10y + 6xy²

A: To find ∂2z∂y2 of z = 2x3-5xy2+x2y3

Q: Calculate ∂ω/∂x for ω=ze(xy^2+2z) Do not include "∂ω/∂x=" in your answer.

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Q: 48xyz < (3x + 2y)(y+ z)(3x + 2z) for every x, y, z E [0, +∞[.

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Q: Express (2xy + 2x – 1) – (x² – y² – 2y)i in terms of z & z, then simplify. - -

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Q: Integrate (1 / (3x + 4)) with respect to x and evaluate the result from x = 0 and x = 2.

A: To evaluate: ∫0213x+4dx We know that ∫1ax+bdx = lnax+ba+C

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: Find dy if x2 + 6xy = 3y2

A: Given: x2+6xy=3y2 If function if f(y) then differentiation w.r.t x is ddxf(y)=ddyf(y)dydx

Q: 87 V 174x-x2 9Vx2+y2 dydx = %3D

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Q: у" — 4y' + у %3D ex + 15

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