(13) If r2 = x2 +y? + z?, then v²r-1 is (a) 0 (b) -r-3r (c) r-2 (d) No

Q: 3 max z = -X1 + 3x2 s.t. X1 - x2 4 X1, X2 2 ()

A: LINEAR programming problem graphical method

Q: y2 2p Thus |g1|+ |92|+ Iaml 3p 0, ((V4p +1-1) (V+1- 2) <0. 1) (vp+1-2) <

A: as given q1+q2+...+qm=3py2 also py2=2p+1-4p+12p              ...i thus, as we know…

Q: 8. What is the particular solution of 2xyy' =1+ y², when x = 2, y = 3 ? C. y =V5x +2 d. y =3x – 4 a.…

A: Given differential equation 2xyy'=1+y2, when x=2,y=3. The objective is to find the particular…

Q: 4 (a) s(-) = -2x + -4x +3x (b) s(<) = 2x° + (c) s(2) = -2(x - 2) (*+ 4) %3D 2.

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Q: The general solution to (D4 – 4D²) y = 0 is O y = c1 + c2x + c3x?e=2# + C4x³e2 + C4x° e2a -2x O y =…

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Q: - a°y°, show that fæy = fyx. 85 Problem - 24: Given f(x, y) =

A: Solve the following

Q: ₁:w+x+y+z=0 ₂:-w+2y=z=14 13:3x-y-2z=4 T₁:7w-x-y+3z=-8

A: to solve the this we use the gauss elimination process to find the solution of the system of…

Q: Consider (D3 + 3D² + 2D)y = 3x2 + 5x + 9. Using method of coefficients, what is y A y = 6x – x2 + 2…

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Q: 4. As an engineer and a scientist, a research has been conducted and the problem has been modeled…

A: We will find out the required maximum value for given objective function.

Q: X1, X2 2 0 12. Minimise Z = 60x1 + 80x2 bo Subject to 20x +30x2 2 900 40x1 +30x2 2 1,200 X1, X220 LO…

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Q: S: z = √x² + y², (x-1)² + y² ≤ 1

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Q: 9-x2 18-22-y2 (x2 + y² + z²) dz dy da? 3 0. x²+y2

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Q: 1 If y* = ex , then y' equals -2x 2y B +3 (c) none of the given choices 2x (D y3 - 2y E x3 A,

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Q: 10--6A Oa) x- -6 V b) x = 6 c)x- 10 V d) x- -2 Oe) x- -8

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Q: n Problems 27–34, find two different pairs of parametric equations for each rectangular equation.

A: To Find: Two different pairs of parametric equations for each rectangular equation 27 y=4x-128…

Q: If y+3y = 8 then g- solution is %3D a- y + 6 = 1 b- In (8 -3y ) = x + c %3D

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Q: 10. Particular solution of y"-4y' + 8y = x³, when x = 0, y = 2, y' = 4

A: We have to find the particular solution of y''-4y'+8y=x3,  when x=0, y=2, y'=4.

Q: 3 x = y + z- w = 2 -x + 2y - z - w = -1 2x - y - z+ w = 4 x + 3y - 2z - 3w = 6

A: 3

Q: (10 – 6y + e-3=) dæ -3.z 2dy = 0 -

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Based on Problem 2, we have the two equations3HK = -p and H3 + K3 = -qSolve for K in 3HK = -p and…

A: Explanation: Given that, 3HK=-pH3+K3=-q   Solve equation (1) for K K=-P3H Substitute the value of K…

Q: If X =V1-t and y= - 3t +t°, what is y' ? O 6(? – 1) /1- O -3 (t? - 1) /1-t %3D 0-6 (t-1)(t + 1) /1-t…

A: x=1-t and y=-3t+t3

Q: Give a particular solution for y" - 2y' + y = 3e".

A: Explanation of the answer is as follows

Q: 9. What is the standard form of 3x(x-3)-D7? а. Зx? — 9х %3 7 b. 3x2 - 3x--7 = 0 d. 3x2 – 9x - 7:= 0…

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Q: The general solution of (D³+4D)y=0 is Ay=ex(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁ex+c₂e²x +…

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Q: 8. What is the particular solution of 2xyy' =1+y², when x = 2, y = 3 ? а. у%3D5x -1 C. y =V5x + 2 b.…

A:

Q: 4. Obtain the general solution (D + D - 9D - Dy = 6e - X 3x + 3xe

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Q: What is the general solution of xy^2dx+x^2ydy=0

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Q: 18. If x² + 2xy = y² then y' is b. 2x + 2y d. -x

A: (18). Given: x2+2xy=y2   We know that; The sum/difference rule: f±g'=f'±g' The Power law:…

Q: a) z=-x² + y² c) z² = x² + 2y² e) x² + y²-z² = 1 b) z=-x²-2y² d) -x² - y² + z² = 1

A: match the following quadratic surfaces with the following equations (a) z=-x2+y2

Q: 7. Given: x + 3y – 2z = 4; 2x + z=-3; and 2y + 3z = -1 What is the value of x + y + z?

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Q: What is the general solution of y"'-3 y"+3 y'-y = e* – x-1

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Q: (10) Ifr² = x² +y² + z², then Vxr is (а) 1 (b) о (c) 3 (d) None of these.

A: r²=x²+y²+z² Then r=xi+yj+zk

Q: 3. Verify that 3e 2x + 4e* is a solution of the y"-3y'+2y=0.

A: We have to verify if the given is a solution to given differential equation or not.

Q: 7. Given: x + 3y – 2z = 4; 2x + z=-3; and 2y + 3z =-1 What is the value of x + y + z?

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Q: If x2 z2 + y² + xz3 = 3, then dz at the point (1, 1, 1) is: O b. Ос. - 3 d. - 3 Ое. f.

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Q: Show that the equation 2³ + 3y3 = 923 has no solution in integers, other than x = y = z = 0.

A: Suppose that, x3+3y3=9z2 has a non-trivial solution, that is other than (0,0,0), and minimal.

Q: 3. What is the particular solution if y(1) = 0 • xy' = y+ (x² + y²) ||

A: Given:- xy' = y+(x2+y2)1/2 y(1) = 0  To find:- Particular solution of given differential equation

Q: Q4 If z = x In(xy) a3 z a4z Find and əy²əx əx²əy²

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Q: 1. A department store has found that its value of sales (2) depends on the mumber of advertisements…

A: Note:- $1=4.17 RM From Part (i), we have The problem is maximum z=420x-2x2-3xy-5y2+640y+1725subject…

Q: 6. What is the general solution of * (x² + 2xy – 4y²)dæ - (2? – 8ay – 4y)dy = 0 a? – 4y = c(x - y)…

A:

Q: The general solution of xy' = -x3³y-csc (xy) is A B C D 2x²cos (xy)+1=cx² -2xcos (xy)² + 1 = cx²…

A: Please see the below picture for detailed solution.

Q: -6r+2y+323D-22 3r+4y+4z= -3 -4r+5y+4z=-29 Note: You can earn partial credit on this problem.

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Q: 5y – 15 What are all the restrictions for v²- 6v +9 y2+ v – 12 ? A x* - 4, x # 5, x*3 B x#3 x* -4 x*…

A: What are the restrictions for 5v-15v2-6v+9÷5v2+v-12

Q: The general solution of æy" + xy' +(3x² – 16)y = 0 for a > 0 is Y = OCiJ/5 (4x) + c2J_va(4x) None of…

A: The Bessel's equation of order ρ is given by  x2y''+xy'+x2-ρ2y=0  Then the general solution of the…

Q: X-3y+z--1 3x-y+2z-2 2x + 3y -z= 1 Eat Ax B A-B 3.

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Q: 2.2 nd, from first principles, fa(3, –1) for f(x, y) = 4x²y² + e®. |

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Q: 27. y 2r(x + 2)² 29. y = x(r - 5)² 31. y = 4x(x + 5)* n= 27r - 2 26. y = x(x - 1)* 28. y = 3x'(x +…

A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost…

Q: x² +1 If y = then y' will be 2х — Зе* 2x(2x + 3e*) - (x² + 1)(2 – 3e*) A. (2x 3e*)? 3 (2х — Зе*) — 2…

A: To find derivative of the given expression.

Q: y "' +y "– 4y'– 4y = 3e – 4x – 6 | |

A: