By using completing the square / dx can be written a V4 + 2x + x² dx 3 + (r+2)? dr 5+ (r+1)² dx V3 + (r+1)? dx

Q: Find in terms of x and y. dx2 x²y2 – 4x = 3 -2xy4 + 4xy² + 4 dy dx2 x

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Q: dx 3. (x+2)Vx+1

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Q: 2. dx (x+1)√x-3

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Q: * x' V5 -x°dx

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Q: .2, Sx² Vx – 1 dx

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Q: e 3. dx V1-e-2* In 2

A: Since we are given with the multiple number of question and kindly repost the other question as next…

Q: If 4x²-2y²=9, then find dy/dx.

A: Using defination of differentiate

Q: a. b. C. [(x² + 2x³ + 4x + 10) dx [ 6xe*² dx [ In x dx

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Q: r10 xe -dx (x+2)(x+3)(x² – 1)

A: Using gaussian 5point quadrature

Q: How to find the implicit differentation of dy/dx=(3xex^2+8)/(y)

A: To determine the implicit differentiation of given function.

Q: Evaluate 1 foto dx. 6 + e-4x -dx 1 6+e - 4x = + C

A: Given : ∫16+e-4xdx To find: Evaluate the given integral

Q: •5 b) 3 -dx x – 3

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Q: Sla 1 z dx |(25 – x²)3/2]

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Q: Evaluate by any applicable method. 1/2 5-x So dx 4x2+1

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Q: Show that -a²x² dx = VT/2a, a > 0, I = e by noting that I = -a²(x²+y³), dx dy -a²r², r dr d0. e

A: We need to show thatI=∫0∞e-a2x2dx=π2a,      a>0

Q: ,3 dx 3 Vx²-16

A: Given integral I=∫x3x2-163 dx

Q: Find if-10x – 6y = -6. dx2 Provide your answer below: %3D dx

A: We Have to find second order derivative

Q: What is the solution of 5 |x - 2|dx

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Q: By using completing the square dr can be written as 4 + 2x + x? dx V4+ (x+2)? dx V5+(r+1)² dx V3 +…

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Q: evaluate using the appropriate method or combination of methods.

A: Factor the denominator

Q: By using completing the square dx can be written as V4 + 2x + x2 dx 3 +(x+2)2 dx V4+(x+2)² dx 3 +…

A: Given, ∫x4+2x+x2dx  We have to write it again using completing the square.

Q: 4 – 2x dx. x3 + 2x2

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Q: By using substitution and integration by parts, find S xe2x dx. (2х-1)2

A: Special Integral (Exponential Integral) : ∫exxdx = Ei(x)

Q: (y + 5 y³) dx

A: To differentiate(1y2-3y4)(y+5y3)

Q: How I show that if Y=ax^2 that (d/dx)=2ax(d/dY)?

A: The given expression is y=ax2.In order to prove the given expression, use the following definition.

Q: An appropriate substitution for 2x dx is V4 – x2

A: The given integral is:∫2x4-x2dx

Q: By using completing the square dx can be written as 4 + 2x + x? dx |3 + (r+1)² dx V5+ (x+1)² dx V4+…

A: Given that a integration and we rewritten this denominator by  using completing square. Now here we…

Q: After appropriate substitution, the integral expression a* (x2 + 4)? dx can be express as (choose 2…

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Q: 2x+1 dx Vx+4

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Q: 1-3x dx Jo J2x-3x² 4. 2х— Зх?

A: Given problem is

Q: b. Find S 5x*(x5 – 1)dx using a suitable substitution.

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Q: By using appropiate substitution, solve dy hpT i. x2 dx 1 = xy – y² ii. – 2. (2х + у)е2»+у | dx

A: Consider the provided question, (b) (i)

Q: ,5. For y = 3x° - 9x° + 2x, find dx %3D dx 5

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Q: Evaluate , Sd-2, r2(1-z) dy dx dz

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Q: valuate. (Be sure to check by differentiating!) 1 dx, x - 3+7x 3/7

A: Evaluate the given integral and check it by differentiation. ∫13+7xdx, x≠-37

Q: TIon 3 By using completing the square, dx can be rewritten as Vx²-4x -7 1 dx V(r-2):-3 1 dx OB. J V…

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Q: Use the trapezoidal rule to evaluate ,2 2х dx % x² +1

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Q: 1 T/ -dx 6 x²+16

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Q: 5. St? V1- t dt (2x+3) dx 6. S (x2+3x-6)

A: Please see the answer below.

Q: By using completing the square dx can be written as /4 + 2x + x2 dx 4+(x+2)² dx V3 + (x+2)² dx V3+…

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Q: Vx2-3 dx , x > V3, is equal to:

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Q: 3x + 1 dx 28. V4 – x2 -

A: Formula used : ∫dx1-x2=arcsin(x)+c

Q: for power substitution method, next step is For S dx xp: 4u³dx 4u³dx 1+ u* 1+ (u*)ã Option 1 Option…

A: Find your answer below

Q: 1. J (5x* - – 4x + 7) dx 8x³ + 6x2

A:

Q: By completing the square, dx the integral S equals: 2x2+8x+10

A:

Q: Sx(2x – 3)®dx

A: Solution

Q: 3) d?y 1zloge %3D dx2 エ マ2

A: There is a correction in the "Answer" provided by you. So I have solved and given a solution with…

Q: luate:J(2x}-1)({3× }-1)dx }denotes. the fractional part.

A: We are asked to evaluate the integral.

Q: Show that dx (a) - x² +1 2

A: Since you have asked multiple question, we will solve the first question for you.If you want an…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.