|2| = (x² + y²)'/2

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Q: 9-x² - y² SS. 0 9-x² 0 √√x² + y² dz dy dx 2

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y * logy x *

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Q: 5. Evaluate the integral 2 c2x x2 (x² + 2y³) dy dx.

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

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Q: e2x-1 If y = prove that = 1- y² dx

A: Given :y=e2x-1e2x+1

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A: We can answer one question as per the honor policy. Please resubmit other question as well to know…

Q: dy = ay + by", dt a > 0, 6 > 0, -∞ < Yo < ∞

A: A differential equation is given by, dydt=ay+by2 for a&gt;0, b&gt;0, y0&gt;0. The objective is to…

Q: 10. f (x) = x² + 4x + 4 Opens up/down:. Vertex: Axis of symmetry: Solution(s): y-int: Domain: Range:

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Q: 7. Solve for dy/dx if x = 2 + t and y = 1 + t2

A: From the given problem: x=2+t;y=1+t2 As we know that the Power law: ddxxn=nxn-1 We know that:…

Q: 8. Jydx + (1+ x)dy = 0,,when x = 1, y = 4

A: Differentiable equation can be solved separating the variables on each side and then integrating…

Q: 18. S V1+x dx 1-х

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Q: 2x+2 dx. 5. x2-2x+1 dy 6. 5. if y = (1+ x²)etan-1x

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Q: -2x y" + (e by = 0 (e-* = z) -

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Q: dey こてxニコッン alx

A: We have to find :- d2y/d2x= ?

Q: solve the differential eq + 2x) dx = = (2y \1+x²y² |dy 1+x²y²

A: The given differential equation is: y1+x2y2+2xdx=2y-x1+x2y2dy

Q: V sin2(x32 - 1) dx, with u x32 - 1

A: Consider the integral ∫(√x)sin2 (x3/2 - 1) dx.

Q: 17. (Vx-x)dx (1-x²) dr 18. 19 o. Sy² dy 20.

A: Given problems:-

Q: dy 5. S: y(1-Vy)2

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Q: 1. f In(x+2) dx 2x+4 2. fx² ex dx 3. f tan³x dx 12

A: We know that integration of xn is xn+1 /n+1. And integration of 1/x is lnx +c.   Here i attached the…

Q: OFind dy 9= (x²45x)"(x + Sec

A: The given function is: y=x2+5x4x+sec x5

Q: x7= - 3x + 18 JZ - 54 in (3+ 57) + c 3/2 2 dx = %3D 3 + VX 3

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Q: 1. S+1)dy y2+4

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Q: Solve the problem by using Exact DE 3 1. (2 x³ x y² - 2y + 3) dx − (x² y + 2 x) dy = 0

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Q: x - 3 7. S V25- (x-2)2 dx 8. S tan5 (2) dy

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Q: 10. x = Vt-2, d²y y =t2-3' dx2

A: The given question is taken from the derivative and we have to find the derivative of the parametric…

Q: 2 1. Z =- 1+x2 ; d²z/dx?

A: z=21+x2

Q: y et 2x *Sec2X Pinel dy o

A: By using these differential formulas that are ddxex=ex, ddxax=axlnx where a is constant,…

Q: -32e* – 140 -dx J e2x +9e* + 20

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: 15) 4S(5x)] = x² , then f'(x) = ? %3D dx

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Q: dy 6. if y = (1+x²)etan-1x

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Q: 17 (7+ x²^ dy when y = dx Find %3| 7 – x²

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Q: d²y 10 9y = e3x + sin 3x dx2

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Q: (3– 3cos5x)} (3x² +2x-7)² (e - sinx +3x) y= Find dy/dx if

A: That's computational, take a careful look.

Q: ſx = s² – t² . z = 2x – 5y, ly =s•t³ · t3

A: We find complex function

Q: By differentiating x² – y² = 1 implicitly, show that d²y | dx² ||

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Q: 1,- X73X+2 dx (x+リ) Izafhinx dx Ax. Iォfュース alx dx X43X+2 X+1

A: Since, you have posted multiple, we will solve only first part. If you want solution of other…

Q: - 3-z2-y 2. Evaluate L* L z dz dy dx -5+x²+y²

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Q: 3) Find d²y/dx² at the point (1, 1), if x6 + y6 = 2.

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Q: 2 - S tần² (3x)sec²(3x)dx

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Q: /25-x2 V25-x2 -y2 1 dz dy dx -/25–x² -V25-x² -y²

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Q: Vaz x² S. (2) dy dx

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Q: Sx² cos (x3 + 3) Van (x3• 3) dx + 3) Vsin (x3+ 3) dx 1)

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Q: 9) (x- y°-Ay-1) dx t 2x (x4 y +2)dy =o

A: As we know that the differential equation Mdx+Ndy=0 is exact, If ∂M∂y=∂N∂x. The solution is:…