2(y+1) dy t 2) 2(у + 1)4 dx x+1

Q: ye(2y*) dy

A: Given the integral I=∫ye2y2dy     ....(1)

Q: The linear approximation at æ = 0 to sin(2z) is A + Bx where A is:| Previev and where B is: |…

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Q: If y = (2x)sin (4z) , then dy sin(4æ) · (2sin(4z) esin(4z) In(x)) %3D dx X synta

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Q: 18y sin3 9y2. 10) +3 cos V9y2 + 3 dy + 3 cos

A: See the attachment

Q: cos² (6y) + sin²(6y) = y + 12.

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Q: Q3) Find dy/dx if 1- y= In x 2- y=x sinx+1-x

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Q: dy dz Find at z = 1 if y = 4z +4 and = 2. dt

A: Given: y=4x2+4

Q: (16x+5y)dx+(3x+y)dy=0, (the curve pass thru the point 1,-3) (3x^2-2xy 3y^2)dx=4xydy (3X^2 - 2Y^2)…

A: Since you have posted a question with multiple questions, we answered the first one for you. If you…

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: 3 хy dx dy 1

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Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: . Find P.S. of (16x +5y) dx + (3x+y) dy = 0 of the curre to pass thru the point (1,-3) 2. Find P.S.…

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Q: EXERCISE 1 dy -dx = 0

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

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Q: Find dy/dx, where xsiny +ysinx=1.

A: Given - xsiny+ysinx=1 To find dydx Here we will use the following formulas- ddx(uv)=udvdx+vdudx…

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

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Q: Find dy/dx of y=sin-(1/,). 9x-

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Q: Get general equation of this DE: (1 + y^2)dx + (x^2y + y + 2xy)dy = 0

A: Solving the DE by seperation of variables

Q: Find dy/dx at the given point. 7x2y4=9-x2-9y  at (0,1)

A: Given: 7x2y4=9-x2-9y We have to find the dydx at (0,1)

Q: Evaluate the integrals

A: We’ll answer the 15th question since we answer only one question at a time. Please submit a new…

Q: 1) ſ y³ sin(2y) dy

A: As per our guidelines we are supposed to answer one question , kindly repost the remaining questions…

Q: sinx So Sa* y dy dx fi dx dy 3. 4-

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Q: Tutorial 14 If y = (sin-1 x)², show that dy (1 – a²) - dy = 2. dx dx?

A: Given, y=sin-1x2 Differentiate with respect to x y'=2sin-1xddxsin-1x=2sin-1x11-x2y'=dydx=2sin-1x1-x2…

Q: tan(3x + 8). Let y : Find the differential dy when x = 5 and dx = 0.4 Find the differential dy when…

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Q: arcsin 4y dy 1 – 16y2

A: Given: ∫arcsin4y1-16y2dy

Q: Find dy/dx in terms of x and y if arctan (x^3)=xy^3?

A: To find the derivative of the given function.

Q: 23, zax + sec(x)cos(y) 0, y(0) = 0

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Q: Find dy/dx at the given point 6x2-5y3=2x-5y at (0,1)

A: First differentiate the equation and then substitute the value of x as 0 and y as 1.

Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: I have stated the used formulas in the solution

Q: Find the general and particular soulution of dy/dx=3y, where y=6 and x=0

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Q: 2sin(y)cos(y) sint(y)+costy) dy

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Q: B. Verify that dz/dy dz/dx 1 =. If xy + z = sinz.

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Q: Ans: y-x+ In y+3, dy = 7. ху+3x-у-3 dx ху-2x+4y-8

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Q: -5 1 -dx Jo 2x+4 1 dt 2 V6-t 1 ii) S,

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Q: 1 of 1 dy -3-9x, y'6)=8, dx² ylo)=2 %3D

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Q: Evaluate dy/dx at x=2 and y=3  if   x4 +  y4 =16.

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Q: S. use "Exact Equation" method (cosxcosy + 2x)dx-(sinxsiny + 2y)dy = 0

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Q: 3. f sin³y(2-3cosy)² dy

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Q: Solve using variaton of parameters or recuction of order (D²-2D+1)y = e" (e*+)²

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Q: , find dy/dx. х • 7x² V2 + cos³t dt 126. y 125. y = V2 + cos³t dt 128. y 127. y = dt 12 + 1 dt 3 + A

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

Q: #2. Show that the line integral (sin y dx + (x cos y – sin y) dy)

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Q: 3. (2х - у - 4) dx - (х-3)dy -0 when x %3 1, y 3D 4.

A: We try to identify and group terms and integrate.

Q: Calculate cln 2 I = Ver – 1 dx thanks to the change of variable u Ver – 1. U = -

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Q: y = In(x +1)

A: Given that : y = ln(x2 + 1). Find dy/dx  We know that derivative of - d(lnx)/dx = 1/x. And d(xn)/dx=…

Q: Find dy/dx of sin^2(3y)=x+y at (2 - pi)/4 , pi/4

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Q: 5. Integrate: S (cose-sin8) de sec 20 6. Find f(3y – y³)ž(1 – y?)dy

A: 5. Given integral, ∫ecosθ-sinθ2sec2θ

Q: dy sin: 8. x +2y = dx y(2) = 1

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Q: cos z dz ar gral f

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Q: The second derivative d^2y/dx^2 of y^3 = xy + 1 at the point (0,1) is

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