4. If x = 1+1 & y==1-t² then dy - at t =1 is dx а) 1 b) 2 c) -1 d) - 2

Q: Differentiate the function y = In (3x² – 6x + 7). Choose the correct setup below to start differe d…

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Q: Solve 2x y da + (x+3y*)dy = 0 Ax'y + xy* = € |9 r*y+y* = c

A: 2x y dx + (x^2 + 3y^2) dy   Here we have to solve the given differential equation:   The given ODE…

Q: 8. dx :) x² +9 0.

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Q: 10. Determine dy of y = 5-2x+7 dx In 5 -2(5-²x+7) ○ (5-2x+7) In 2 ○ (5-²*+7) In 5 ○ 2(5-2x+7) In 2

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Q: (2xy-3x²) dx + (x ² + 2y) dy = 0

A: As we know that; The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution…

Q: (1 –2²)dz

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Q: Finds 2) S 12x-31 dx

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Q: Differentiate y = VIn x 2 Inx +1 A. 2(In x)2 3. Inx-1 3 (In x)2 2 Inx-1 C. 2(In x)2 13 1. D. 3) 2(In…

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Q: Find dy/dx given xy2 + x²y5 – x³ = 3 %3D -

A: Given that : xy2 + x2 y5 - x3  = 3. Find dy/dx . We know that d(xn)/dx = nxn-1.   Here i attached…

Q: S. dy |1+5

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Q: Calculate using polar coordinates. √4-7² 2 siste o x² + y² dy dx

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Q: 2x-2y+1 5) y' = x-y

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Q: 2 Find So (3x2 + 4y³) dy dx.

A: Topic:- double integration

Q: 4. (D2 – 5D + 6)y = 15sinx – 15cosx -

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Q: 2) 3. | 24 ly-11 dy

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Q: dx tan x -1 '+ 4dx de x- Vx

A: Taking #5 and #6 As per authoring guidelines, if the question number is not specified, the first…

Q: 5-find Аху : xe 12) if f(x, y) = xe

A: First I have mentioned what we have to find then just use the rule of partial derivative find the…

Q: Evaluate the to -y dxd

A: Given that, the integral is ∫01∫01-y2x2+y2dxdy. Obtain the value of ∫01-y2x2+y2dx.…

Q: d) S 2xe* dx

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Q: 10. (D² – 3D) y= 9x² = 9x2

A: 10) Given Information: Given differential equation is D2-3Dy = 9x2

Q: Find dy -, if dx dy dx y = u U³ || - u and u = 4x² + 1.

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Q: Y = 4x²-5 Vsx dy=?

A: We want to find derivative of y, The given expression for y is,               y=4x5-55x

Q: dy Q2) Solve x- 2y = x³ cotan 2x dx

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Q: 4. Find dyax and d2 x =V4- t , go t²-2t ye t'-2 get'.

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Q: [° [² (5 x² + y²) dx dy

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Q: A) B) dx₁ dt dx₂ dt dx₁ dt dx2 dt dx₁ dt dx₂ Wh = x₁ + 2x₂ + 2x₁.x2 = x₁ + x₂-X1X2 is stable or…

A: Given :           A) dx1dt=x1+2x2+2x1x2    dx2dt=-x1+x2-2x1x2           B) dx1dt=-x1+x2+x12…

Q: Q3 / Find d²y/dx² for the following; (5sec 3x) 2. x = t - t3, y = 2t + 5 1. d? dx2

A: The term represents the second derivative of the variable y. It can be obtained by differentiating…

Q: Evaluate

A: Using fundamental theorem of calculus, to find the derivative of definite integral, one need to plug…

Q: 7. (D³ — 2D² − 5D + 6)y = 0; y = 1, Dy = −7, D²y = 1 when x = 0

A: The given equation is;  (D3-2D2-5D+6)y=0, y=1, Dy=-7, D2y=1 when x=0.

Q: 2. +x +1 d

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Q: 23. If exy = 3, then what is Y at the point (1, In3)? dx -In3 3ln3 In3 -4In3

A: Given:- exy = 3 To find:- dy/dx at point (1,ln3)

Q: 9) y = e4x² + x A) dy dx 8xe2x + 1 B) dy - 8xex2 dx %3D + 1 C) dy dy - 8xe4x2 dx — 8хе + 1 %D D) + 1

A: We have to find

Q: 7 4) (y + x^²³² ) dx =xdy

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Q: (x+6) 15. J (x+2)2 dx

A: Here I am attaching image so that you understand each and every step.