(w³ + wz² – z)dw + (z³ + w²z – w)dz = 0

Q: f(x, y, z) = 3x - 2y + z- 12 = 0 g(x, y,z) = 4x + 2y - 25 = 0 h(x,y, z) = x- y²z-7= 0

A: Use the following formulae, to find the approximate solution of the non-linear system by the Newton…

Q: 3. f(x, y) = (3x - 5y)2 + e4x In(4y – 9) + %3D 135 x4

A: We know, ddxxn=nx(n-1)  , for any real number n. ddxln(x)=1x

Q: z" + 6z' + 8z = e – 6u(t – 3); z(0) = 2, z'(0) = - 6 %3D

A: Laplace transforms

Q: E R -2x - 6 M NL = %3D 2x – 14 SR = I+ 15 x+2 wV = x+21 F FD WN = 4y x + 4 6(y -1) 4x -2

A:

Q: if z=x+iy then zz= 3- y² +1 3- y² – 1 G- ² |

A:

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: (x.yız) (x,9e)x4か t. 22 P( 3-1,0) けこくりん)2

A:

Q: Non Homogeneous: (D2 − 7D + 6)y = 3x2 − 2x + 5

A: Here we have to solve the non-homogeneous differential equations     (D2-7D+6)y = 3x2 - 2x +5 .

Q: 3 '9-x2 3+V9-a2-y? 1 dz dy x² + y² x²+y² a C = L7I Fle,0,6) dp dộ do

A:

Q: (D³– 4D°D'+ 5DD2 – 2D ) z = e'*2* + Vy + +2x +Vy +x. |

A:

Q: (3x)i + (3y)j + (3z)k F = x3 + y3 + z3

A:

Q: a z = 4x³-6x²y²-y com x= 2sen(t) y=-3cos(t) e

A: #As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: (w² – z² – 4z – 1))dw + 2w(z + w + 2) dz = 0

A:

Q: 2. x3 - y3 = c³, find y" %3D HOOAT d²x 3. x* = at?, find dt2 1983

A:

Q: Minimize c = r + 2s + 3t 3r + 2s + t > 60 Subject To: 2r + 3t > 60 And Where: {r > 0, s > 0, t > 0}…

A: According to the given information it is required to solve the given problem:

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: B. Non- homogeneous Higher Ordered LDE 2 1.D +50² + 8D -9) y - 69x²e-*

A:

Q: 2. y" – 2y' – 3y = e²", y(0) = 1, y (0) = 0, Yp(t) = -e2' /3 %3D

A:

Q: S (x,y.:)= 4x°y° -e°y* ++4y-x" +4y–x'6

A: It is partial derivative

Q: 33. Y"(t) - 8Y(t) + 2Y(t) = 4t + 12e-t, Y(0) = 6, Y'(0) = -1. %3D Ans. Y(t) = 3ef-2et+ 2t + 3+2e-

A:

Q: 1 dz, C:k – 3i] = 3 z² +4z + 13

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 3. 2. Z dydxdz 2=0 X=Z

A:

Q: f(z) dz = 4, then 2f(x) – z dz 13 If %3D =

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Q: W = / x2 + y² + z² Find Wx, Wy, Wxz,Wyy, Wzyx %3D

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Q: dz (D2 + 16) (D² + 4D – 5) (D² + 2D - 3)*z = 0, Dz = dr

A:

Q: Determne y (8x +3)/2 from (11)/2 s ys (27)2?

A: Given: y=(8x+3)32     from 1132≤ y≤2732

Q: Find f2, fy, and f.- f(x, Y, z) = (4x² + 6y² + 3z²)¯05 fz = fy = f. =

A:

Q: 1- z Res z(z + 1). Iz=00 a) 0 b) 1 c) -1 d) 2 ||

A: Res( f, ∞) = - Res 1z2f1z, 0

Q: 3x + y + z = -2x - y x + 3y - Sz - 11 -7 A. (2, 3, t) В. (2, 3, 0) OC. (2 +t, 3 - 2t, t D. (2 - t, 3…

A: A general system of m linear equations with n unknowns can be written as {\displaystyle…

Q: dz If x4 – y4 + z - 3z = 2, then %3D %D dx a) 4x3-4y3 3-4z3 b) 4x3 3-4z3 c) None of these d) 4x3+4z3…

A:

Q: (w°t wz? -z) dw +(z² tw² -w) dz= 0

A: Let's find.

Q: y = -2x-22 tl X-2y-z+2 (37) Zニ X-y 2x +y +2z = I x+2y +z=2 2 -L

A:

Q: x+3y+z=90     7y+2z=56 Using the echelon method

A: observe that the number of variables is great than the number of equations. So, one of the variables…

Q: 2x + y + z = 1 X- y+ 4z = In1 x + 2y – 2z = 3

A:

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

A:

Q: 2x + y + z = 1 X- y+4z = In1 x + 2y - 2z = 3

A: We will solve this equation with the substitution method. So first of all we will find anyone…

Q: f(x, y, z) = V9 - x² – y2 – z²

A: The given problem is to find the surface for the given function of three variables. Given function…

Q: z = 2 24 z=Vx² + y² 2 FIGURE 9

A:

Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: C(-4,0) andr = 3 (x – h)2 + (y - k)2 = r2 0 = 1 + + +A + zX

A:

Q: z(z² 2). 9. y Ans. dy -1 dz (z + 7)* dy 1 Ans. dz (4 z) 2y 11. 12 ong b Ey - 2 - 3z 3z - 1 Ans. y =…

A: The derivative is calculated mainly using quotient rule.

Q: 4. (D3 – 4D² + 4D)y = 0 5. (2D4 – 3D3 – 2D²)y = 0 - -

A: (4). The given differential equation is: D3-4D2+4Dy=0 So, the auxiliary equation is: m3-4m2+4m=0

Q: 18. (9x D² + 3xD + I)y = 0, y(1) = 1, y'(1) = 0

A:

Q: 2) (r'y-2y kdx+ (y`x- 2x* \dy = 0

A: 2) Given that, x3y-2y4dx+y3x-2x4dy=0y3x-2x4dy=-x3y-2y4dxdydx=2y4-x3yy3x-2x4           ...(1)

Q: (D² – 4)y = 2 – 8x; when x = 0, y = 0, y' = 5. %3D ANS. y = e2x – e-2* + 2x – }.

A: We have to find solution of given differential equation.

Q: Minimize c=s+ 2t subject to 4s +t2 270 2s +t2 190 s+ 3t 2 330 s20, t2 0. C = (s, t) =

A: The given minimize problem is C=s+2t subject to constraints, 4s+t≥2702s+t≥190s+3t≥330s≥0, t≥0   Then…

Q: Find E[Y(z)] when Y(z) is given by 2z' + 6z² + 5z + 1 2(2z + 1)

A:

Q: D’(D² – 4)y = 3x+ 2e¬3* | y = 3x + 2e¬3x m° – 5 - 4m³ = 0 ® m' (m2 – 4) = 3x+2e-3* D (D² - 4) = 0 3…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.