SOLVE THE EQUATION. SHOW YOUR COMPLETE AND CLEAN SOLUTION. 2 (x – y) dx + dy = 0 O x + In[2 (x – y)] – 1 = C | O x + In[2 (x – y)] + 1 + C O x - In[2 (x – y)] + 1 = C O x - In[2 (x – y)] – 1 = C

Q: A. Using the basic formulas, integrate the following: 1. S(x* – 2x3 + 3x? – 1)dx 2. S(2x – 5)?dx 3.…

A: Explanation of the answer is as follows

Q: •2 1 -dx- J-3 (x + 7)(x² + 16)

A: Given integral is Apply partial fractions to break the denominator

Q: Solve the D.E. 3(3x? + y²) dx - 2xy dy = 0 (A x= c(x² + 9y²) B x= c(x2 + 3y3) © x = c(9x² + y²) D x…

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Q: Step 4 Finally, determine(-3x + 7) and (x + 7) and simplify the result. dx dx 1. du 1 dv + U dx V dx…

A: formulas we use: ddxf+g=dfdx+dgdxddxkx=k; k is a constant.dkdx=0; k is constant.ddx(x)=1.

Q: Solve for a2f дхдz if f (x, y, z) = x³=3y

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Q: + y²(x+ 1)² = C

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Q: Solve the equation using Reduction of Order (D² - 5D + 6) y = 2e* Oy=e+c₁e²x + 2c₂e³x Oy = √² + ₁³x…

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Q: Compute dx. X + 2 *+ C Ox-2in|x| +C + C 2+ 2x Ox-2injx + 21 + C + C (x + 2)2

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Q: Find D,y, given y = 3e" (2x – 5)*. D.y = 3e [4(2x– 5)'(2)]+(2r-5)'(3e") = 24e" (2x – 5)' + 3e"…

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Q: If x? – 2x – 3 = (x+ A)² – B² , then the value of Bis %3|

A: Given that   x2-2x-3=(x+A)2-B2,  we have to find the value of B. To solve the problem we first…

Q: Solve (√x+x)=√y+y Select one: O a. y (c(1+√x) + 1)² O b. y = (c(1+√x)-1)² O cy=(-c(1 + √x) + 1)² O…

A: The given equation is; [sqrt(x)+x]dy/dx=sqrt(y)+y.

Q: Evaluate -42 (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7) X

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Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7) 323 2

A: Here to find the value of line integral we consider two path c1 :from the point (0, 0) to (0, -7)…

Q: = / y ²³. (X²+1) (3x+4) 5/ (2x-3)(x²-4) Find dy da

A: To find dydx:

Q: dy et + 4x Find if y = The answers have been slightly simplified. %3D dx 3x – 1 (3x – 1) (e² + 4) +3…

A: The given equation is y=ex+4x3x-1.

Q: Calculate (2x+3y+z)dV where = [1,2] x [-1,1] × [0,1] A. 0 B. 1 C. 4 D. 7

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Q: 2 dy 67 +13

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Q: Determine for which values of m the function (x)=x" is a solution to the given equation. (a) 3,2d…

A: We have to find the value of m.

Q: Find the general solution to(D5 - 2D3 – 2D2 – 3D - 2)y=0

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Q: cln3 dx (b) (10 points) Ф) (10 роints) z et n2 e*-e

A: We use the definition of the integral of functions and partial fractions to evaluate the given…

Q: Find dydx for…

A: the given equation of the curve is: y3+y2-5y-x2+4=0 we have to find the value of dydx

Q: Solve: (3x? – 2xy+ 3y² )dx = 4xydy O (y – 3x) (y + x) = Ca³ O (y + 3x)³(y – x) = Ca³ O (y – 3x)(y +…

A: Proceed as shown below

Q: 2x +1 (ii) Sa. dx . 6x² + x – 15 (ii) J

A: We first factor the denominator

Q: The linearization of_z = y√x_atx=16 and y=1 is

A: Linearization is defined as the finding of a linear approximation to a given function at a given…

Q: Evaluate / (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (7, -5)

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Q: Find the change of variable x = Py that transforms the quadratic form x Ax into y Dy as shown. -…

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Q: Convert to standard form. y = (x – 3)² – 16

A: